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		<title>Scientific Explanations for Remote Viewing</title>
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		<pubDate>Fri, 04 Jun 2010 14:34:37 +0000</pubDate>
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		<description><![CDATA[Eighteenth and nineteenth century physical science had completed and embellished the &#8220;golden age of a mechanistic and deterministic models of the universe&#8221; where the universe and its constituents are ruled by rigid interactive forces that can be measured, phenomena that can be predicted using mathematical tools, and where the universe or any system operating within [...]


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			<content:encoded><![CDATA[<p>Eighteenth and nineteenth century physical science had completed and embellished the &#8220;golden age of a mechanistic and deterministic models of the universe&#8221; where the universe and its constituents are ruled by rigid interactive forces that can be measured, phenomena that can be predicted using mathematical tools, and where the universe or any system operating within it is made of the sum of its parts.</p>
<p>Light was thought to be an electromagnetic wave vibrating in an undetected, and later experimentally disproved media: &#8220;the ether&#8221;, at certain rates of vibration that would define its color. It was part of the electromagnetic wave spectrum that allowed one to perceive an electromagnetic wave as heat, light , radio waves, or other electromagnetic radiations depending on the frequency of its vibrations. This spectrum had been well-defined by the equations of the English physicist James Clerk Maxwell in 1864.</p>
<p>Man&#8217;s biology was reduced to a mechanical system albeit of extreme complexity, and thought was perceived to be but an epiphenomenon of the mechanical brain.</p>
<p>All this was very hygienic, logical, and comforting. It allowed to view the so-called invisible world of spiritual forces or entities as a personal unproven hypothesis, and permitted the justification of atheistic concept to be scientifically sound. Basically it allowed for purely atheistic politico-philosophies alike communism to find a sympathetic resonance within the &#8220;intelligentsia&#8221; and the masses.</p>
<p>It also gave a great mechanistic impetus and approach to the fields of biology, microbiology, psychology, neurobiology, and the allopathic technical mechanistic approach to the health sciences. Technology was &#8220;king&#8221; and the understanding of interactions between well-defined separated systems would bring the possible conquest of disturbances and imperfections in the &#8220;machinery&#8221; of biological entities.</p>
<p>Man having created a new religion called &#8220;science&#8221;, which revered himself and his intellect, had the perception of having attained a Godlike control over nature.</p>
<p>By the end of 19th century the ultraviolet catastrophe &#8211; as it came to be known &#8211; put this whole hygienic view of the world in question, and the theory of &#8220;quanta&#8221; of Max Planck was introduced in 1900. The German physicist Max Planck introduced the notion of packets of energy that he called &#8220;quanta&#8221; in order to explain why the wavelength (color) of the radiation given off by heated objects did not rise in a continuous manner but in discontinuous spurts from value to value as they grew hotter. Danish physicist Niels Bohr, who was to become later one of the fathers of the &#8220;Manhattan Project&#8221; that developed the first US A-bomb during WWII, used in 1913 the theory of &#8220;quanta&#8221; of energy in order to prove that the whole world of atoms was full of &#8220;quantum&#8221; jumps. An electron could jump from one level of energy (so-called orbit) to another without appearing in-between these states. Discontinuity had been introduced in our equation of the universe!</p>
<p>In 1905 Albert Einstein defined light as made of quanta of energy or particles that he coined &#8220;photons&#8221; in his famous paper explaining the photoelectric effect for which he received a Nobel prize in 1923. He nevertheless acknowledged that light could also be defined as a wave, depending on the mode of observation used in a chosen experiment, and the particle/wave duality was introduced in our attempts to grasp the mysteries of nature.</p>
<p>The new physics of the beginnings of the twentieth century gave a mortal blow to the deterministic principles of the old school of thought. Time and space became relative notions according to the theory of relativity of Albert Einstein. Quantum physics stated that all particles of matter could be viewed either as material bodies or as waves. It allowed for one electron (or any other particle) to be in two locations at once (double slit experiment), and proved that one could not predict the next location of a particle by knowing its present one.</p>
<p>In the strange world of quantum physics, particles dematerialized themselves into waves (such as in transistors) and rematerialized themselves later into particles. This depended on the type of experiment they were subjected to, and most importantly: the choice made by a conscious observer as to how he or she would view these particles.</p>
<p>To most theorists, the phenomena of nature existed only as determined states as a conscious observer witnessed them, either directly, or through the artifacts of a measuring device. Quantum mechanics was born, and with it our view of reality would be forever changed.</p>
<p>In order to comprehend events in the phenomenal world, one needed to introduce a major variable that had until then been ignored: The consciousness (self reflective thought) of the observer. Without the perception of a material world by a conscious entity, there were great doubts as to the existence of that material reality independently of its observation.</p>
<p>In other words we make a potential reality manifest itself by our choices, even retroactively through time and immediately across the perceived infinite space, as the two experiments mentioned hereafter have proven, to the surprise of most physicists. Or, in other words, volition and free will operate outside the confines of time/space, and our impression of making choices is but a delayed awareness of events that higher levels of our minds have already made for us and therefore project to our awareness (ego) as a holographic packet of sensory information, post facto. We are therefore, at a higher level, the maker (subject) of our reality projected to one&#8217;s self (object) within the web of probabilities of the quantum world that we &#8220;materialize&#8221; for both the subject and the object that are but two mirrors of one same reality: Consciousness, defined as self -reflective awareness.</p>
<p>Very advanced &#8220;remote viewers&#8221; know at which points volition is part of the higher levels of one&#8217;s self and at which points it is made available to the lower (conscious level), as the quantum self or higher self merges with the lower self (ego).</p>
<p>Our courses attempts to allow the conscious part (reactive sensory apparatus operating as intellect) and the much higher vibratory mind (deep subconscious level) to merge with each other in awareness in order to allow a human individual to be more in control of one&#8217;s reality and probable future. At the level of the higher mind time/space is instantly bridged. &#8220;Remote Viewing&#8221; and especially &#8220;Remote Influencing&#8221; allows one to connect to that level.</p>
<p>Mr. O&#8217;Donnell only mentions quantum physics in order to allow for the comforting view of reality of most individuals to be shattered and at the very least questioned. Each one is to find his or her own truth, using eventually his or her own path. The course is only meant as a guide to a new world, an opening to a new way of viewing and experiencing reality.</p>
<p>In 1982 at the Institute of Applied Physics and Theoretical Optics at the University of Paris, France, the team of physicists composed of Alain Aspect, Jean Dalibard and Gerard Roger made what may prove to be the greatest scientific discovery of this century. They proved experimentally that the world is non-local or non-separable. This is equivalent to saying that space, as we perceive it to be, does not exist, but is an illusion of our senses. Projected by whom? This is the big question that science tries to answer.</p>
<p>In the same field of quantum theory, time is not only relative but one can experimentally change the past, as the delayed choice experiment, carried out by scientists in the 80&#8217;s at the University of Maryland and the University of Munich has proven.</p>
<p>Although this all seems to belong to the realm of science-fiction, it is a reality, albeit hard to accept, for all the minds that dwell in the world of the quanta: a world full of seemingly contradictions, surprises, and a certain sense of humor.</p>
<p>All modern disciplines are nowadays affected by it, short maybe of modern biology, neurobiology and surprisingly psychology that are still embracing a mechanistic view of thought and have not, as yet, been able to define it.</p>
<p>Quantum physics gave us the invention of the atomic bomb, the transistor, the computer chip, laser and devices using laser light as a conduct for information, Josephson junctions in supercomputers, superconductors etc.</p>
<p>You should never doubt your natural-born ability to operate at such a high vibratory level of thought. This ability has been proven since antiquity, and is still utilized successfully by highly secretive intelligence units belonging to the major world powers.</p>
<p>This is one case where a dose of skepticism in the field of thought orientation and exploration is unhealthy, and the fear of ridicule even more so. You have to become open-minded, as a child is. All major shifts in scientific thought have incurred the ire of the static-minded old Praetorian Guard of proven inadequate sclerotic systems that are beginning to hit too many walls loaded with points of singularity.</p>
<p>The methods taught in our courses are probably part of the dawn of a new paradigm shift in scientific thinking that will revolutionize and change the &#8220;old classical scientific concepts&#8221; of the late 19th century that still rule for most of us our interpretation of our perceived material reality. This will have major implications in the natural and health sciences, the biological perceptions and their assumed correlations, all other phenomenal science, and the understanding of what the mind is.</p>
<p>If we are in the process of constantly creating our reality by thinking about it in an individualized and global manner, and that science reflects but a snapshot of our attempt at understanding our Creation, a major shift in our thought- perception will induce totally different ways at experiencing the phenomenal world and controlling it to our desires.</p>
<p>All aspects of our lives in this new Millennium will, most likely, be profoundly transformed by it.</p>
<p>The introduction of consciousness as a major factor in the equation of reality by modern quantum physics is at the core of one of the major paradox of so-called psychic research. According to quantum physics, the thought of the observer has an influence upon the result of an experiment. Therefore, if we are co-creator of our reality by mere thought, the natural imbued skepticism of many scientists and their methodologies introduce a negative bias in the results that they would obtain in thought experiment such as &#8220;remote viewing&#8221; etc.</p>
<p>In other words, in order to achieve 100% success at proving the efficacy of &#8220;remote viewing or influencing &#8221; one would need to deal with scientists and tests subjects that are of the firm belief of the easy achievement of such mental feats, which would automatically be called a bias experimental protocol by the skeptical scientific community. That is why the best results at remote viewing were always achieved within intelligence and military secret units that pragmatically only cared about bridging time and space effectively using mental technologies, and were not the least concerned about peer recognition and the fear of being ridiculed. <br/><br/><span id="more-500"></span>
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		<title>Albert Einstein » Quantum Entanglement – The Weirdness Of Quantum &#8230;</title>
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		<pubDate>Fri, 04 Jun 2010 03:03:02 +0000</pubDate>
		<dc:creator>Material Geek</dc:creator>
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		<description><![CDATA[Quantum mechanics holds that observables, for example spin, are indeterminate until some physical intervention is made to measure an observable of the object in question. In the singlet state of two spin, it is equally likely that any given particle will be observed to ...


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			<content:encoded><![CDATA[<p>Quantum mechanics holds that observables, for example spin, are indeterminate until some physical intervention is made to measure an observable of the object in question. In the singlet state of two spin, it is equally likely that any given particle will be observed to &#8230;</p>
<p><span id="more-499"></span></p>
<p>Read this article:<br />
<a target="_blank" href="http://alberteinstein.strips4you.com/?p=6255" title="Albert Einstein » Quantum Entanglement – The Weirdness Of Quantum ...">Albert Einstein » Quantum Entanglement – The Weirdness Of Quantum &#8230;</a></p>
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		<title>Albert Einstein » Quantum Entanglement – The Weirdness Of Quantum &#8230;</title>
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		<pubDate>Fri, 04 Jun 2010 03:03:02 +0000</pubDate>
		<dc:creator>Material Geek</dc:creator>
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		<description><![CDATA[Quantum mechanics holds that observables, for example spin, are indeterminate until some physical intervention is made to measure an observable of the object in question. In the singlet state of two spin, it is equally likely that any given particle will be observed to ...


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			<content:encoded><![CDATA[<p>Quantum mechanics holds that observables, for example spin, are indeterminate until some physical intervention is made to measure an observable of the object in question. In the singlet state of two spin, it is equally likely that any given particle will be observed to &#8230;</p>
<p><span id="more-498"></span></p>
<p>Read the original:<br />
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		<title>Quantum Mechanics: Properties Of Elementary Particles &#124; ScreenGuide</title>
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		<pubDate>Thu, 03 Jun 2010 11:44:07 +0000</pubDate>
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		<description><![CDATA[Strictly speaking, the term particle is a misnomer because the dynamics of particle physics are governed by quantum mechanics . 


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			<content:encoded><![CDATA[<p>Strictly speaking, the term particle is a misnomer because the dynamics of particle physics are governed by quantum mechanics . </p>
<p><span id="more-497"></span></p>
<p>Excerpt from:<br />
<a target="_blank" href="http://screenguide.com.au/2010/06/03/quantum-mechanics-properties-of-elementary-particles/" title="Quantum Mechanics: Properties Of Elementary Particles | ScreenGuide">Quantum Mechanics: Properties Of Elementary Particles | ScreenGuide</a></p>
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		<title>Shock Wave Black Cloth Shin Instep Pads Reviews « Inside MMA</title>
		<link>http://wave-mechanics.materialgeek.com/shock-wave-black-cloth-shin-instep-pads-reviews-%c2%ab-inside-mma/</link>
		<comments>http://wave-mechanics.materialgeek.com/shock-wave-black-cloth-shin-instep-pads-reviews-%c2%ab-inside-mma/#comments</comments>
		<pubDate>Thu, 03 Jun 2010 07:29:56 +0000</pubDate>
		<dc:creator>Material Geek</dc:creator>
				<category><![CDATA[Wave Mechanics]]></category>
		<category><![CDATA[A Shin Kick]]></category>
		<category><![CDATA[A Thai Kick]]></category>
		<category><![CDATA[Dojo]]></category>
		<category><![CDATA[Kumite At The]]></category>
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		<description><![CDATA[During kumite at the dojo, the lightning shin guards kept sliding off every time I'd land a shin kick, or block a thai kick with my shin (including proper mechanics of leg movement). This resulted in the lightning pads' ineffectiveness


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			<content:encoded><![CDATA[<p>During kumite at the dojo, the lightning shin guards kept sliding off every time I&#8217;d land a shin kick, or block a thai kick with my shin (including proper mechanics of leg movement). This resulted in the lightning pads&#8217; ineffectiveness</p>
<p><span id="more-496"></span></p>
<p>See the original post here:<br />
<a target="_blank" href="http://www.twinsspecial.org/mma/shock-wave-black-cloth-shin-instep-pads-reviews/" title="Shock Wave Black Cloth Shin Instep Pads Reviews « Inside MMA">Shock Wave Black Cloth Shin Instep Pads Reviews « Inside MMA</a></p>
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		<title>Vessel Delay Analysis</title>
		<link>http://wave-mechanics.materialgeek.com/vessel-delay-analysis/</link>
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		<pubDate>Thu, 03 Jun 2010 00:41:45 +0000</pubDate>
		<dc:creator>Material Geek</dc:creator>
				<category><![CDATA[Articles]]></category>
		<category><![CDATA[Analysis]]></category>
		<category><![CDATA[Delay]]></category>
		<category><![CDATA[Vessel]]></category>

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		<description><![CDATA[Delay analysis    There are numerous historical well as recent and predictive datasets. System that provides real-time information about water levels, currents, and other oceanographic and meteorological data from bays and harbors “Now casts” and predictions of these parameters with the use of numerical calculation models are available. In certain locations this information is [...]


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			<content:encoded><![CDATA[<p>Delay analysis  <br/><br/>  <br/><br/>There are numerous historical well as recent and predictive datasets. System that provides real-time information about water levels, currents, and other oceanographic and meteorological data from bays and harbors “Now casts” and predictions of these parameters with the use of numerical calculation models are available. In certain locations this information is very important to track because changes to the bathymetry due to dredging or as a resulted in changes in water currents or other oceanographic effects.  <br/><br/>  <br/><br/>A program by ….is capable of predictions of ship motions (i.e. displacements, velocities, and accelerations) for a ship advancing at constant speed, on arbitrary headings in both regular waves and irregular seas. The irregular seas are modeled using either the two parameter like Bretschneider, the three parameter Jonswap, or the six parameter of Ochi-Hubble wave spectral models. Both long-crested and short-crested results are provided; short-crested waves are generated using a cosine squared spreading function. In addition to the 6DOF responses, will predict the absolute motion, velocity, and acceleration, as well as the relative motion and velocity for various locations on the ship. SMP95 will calculate the probabilities and frequencies of submergence, emergence, and/or slamming occurrence for various locations on the ship. It also incorporates recent innovations for calculating added resistance in waves based on the work by Wen-Chin Lin and Arthur Reed, as documented in their paper &#8220;The Second Order Steady Force and Moment on a Ship Moving in an Oblique Seaway&#8221; <br/><br/>  <br/><br/>  <br/><br/>Standard power <br/><br/>  <br/><br/>Navigation is typically formulated to provide safe and efficient passage for a selected ship under specified transit conditions. The design ship and transit conditions may be selected to represent the “maximum credible adverse situation,” the worst combination of conditions under which the project would be expected to maintain normal operations. A project that successfully accommodates this situation can be expected to perform well with a full range of smaller ships and less difficult transit conditions.  <br/><br/>(1) Design vessel &#8211; For deep-draft projects, the design ship or ships are selected on the basis of economic studies of the types and sizes of the ship fleet expected to use the proposed channel over the project life. The design vessel or vessels are chosen as the maximum or near maximum size ships in the forecast fleet based on the characteristics (length, beam, draft) of the ships being most representative of the potential economic advantage to be found in the forecast ship fleet.&#8211;For small craft projects, the design vessel or vessels are selected from comprehensive studies of the various types and sizes of vessels expected to use the project during its design life. Often, different design vessels are used for various project features. For example, sailboats, with relatively deep draft, may determine channel depth design; and fishing boats, with relatively wide beam, may dictate channel width design. <br/><br/>  <br/><br/>(2) Operational conditions selected for design can strongly affect a navigation project. A deep-draft project should be designed to allow the design ship to pass safely under design transit conditions. Normally, extreme events are not considered in specifying design transit conditions. Ship operators can usually suspend operations during these rare events without undue hardship.  <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>(a) Operational factors to be specified for design transit include: <br/><br/>• Wind, wave, and current conditions. <br/><br/>• Visibility (day, night, fog, and haze). <br/><br/>• Water level, including possible use of tidal advantage for additional water depth. <br/><br/>• Traffic conditions (one- or two-way, pushtows, cross traffic). <br/><br/>• Speed restrictions. <br/><br/>• Tug assistance. <br/><br/>• Underkeel clearance. <br/><br/>• Ice. <br/><br/>  <br/><br/>Normal operational conditions are strongly influenced by individual, local pilot, and pilot association rules and practices. For example, pilots usually guide a transit only when conditions allow adequate tug assistance. There may be operational wind, wave, or current limitations on the ability to safely moor a ship at a terminal or berth. Turning operations and maneuvering into a side finger slip may be limited by tide level and current conditions, including river outflow. Energetic wave conditions at the seaward end of the entrance channel may prohibit pilots from safely transferring between the pilot boat and ship. Such operational limitations may well be controlling factors in determining whether or not a safe transit is possible, and navigation project design should be consistent with these limitations. <br/><br/>  <br/><br/>Ice navigation. Winter conditions along northern sea coasts, estuaries, and large lakes can cause ice to be an occasional, if not chronic, concern for safe and efficient navigation About 42 percent of the earth experiences temperatures below freezing during the coldest month of any year. The presence of ice is accompanied by longer nights and increased fog and precipitation. Shipboard mechanical equipment, instruments, and communications apparatus are less efficient and more prone to failure in cold temperatures. Aids to navigation become less effective, and maneuvering in ice is much more difficult, hence ships experience difficulties. Sea ice nomenclature and map notation symbols are defined by the World Meteorological Organization (WMO 1970). Ice thickness and structure are key concerns. Multi-year ice, sea ice more than 1 year in age, can be over 3 m thick, but it is found only in the Arctic Ocean and its marginal seas and near Antarctica.  Therefore ships that regularly navigate icy waters must have exceptional structural strength and propulsion power for safety of the crew, equipment, cargo, and environment. Special hull, propeller, and rudder designs reduce resistance and help clear lanes.  <br/><br/>  <br/><br/>Icebreakers may be needed to escort ice-strengthened cargo vessels or to periodically clear shipping routes.Factors to be considered for ship operation in ice rather than temperate conditions are: <br/><br/>• Ship maneuverability is retarded. <br/><br/>• Ice forces can divert ships from their intended course. <br/><br/>• Darkness is more common. <br/><br/>• Low visibility is more common (fog and precipitation). <br/><br/>• Winds can be very strong. <br/><br/>• Visual aids to navigation are less effective. <br/><br/>• Shipboard instruments are more prone to malfunction. <br/><br/>• Assistance or rescue by tugs is more difficult. <br/><br/>• Crews are more strained and fatigued in the face of these challenges. <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>Standard displacement and trim <br/><br/>  <br/><br/>Design draft is the distance from the design waterline to the bottom of the keel. Ship depth is a vertical dimension of the hull, as shown in the figure, and it should not be confused with ship draft.  Draft may not be uniform along the vessel bottom for both deep- and shallow-draft vessels. Normally, draft near the vessel stern (aft) is often greater than near the bow (fore). Two useful indicators of such variations are: trim &#8211; difference in draft fore and aft, list &#8211; difference in draft side to side. Maximum navigational draft is the extreme projection of the vessel below waterline when fully loaded) is needed for navigation channel depth; mean draft is preferred for hydrostatic calculations. Waterline beam (width of the vessel at the design or fully loaded condition necessary for navigation channel width. Maximum dimensions of the above-water part of a vessel are also critical to ensure adequate clearance. Maximum beam is the extreme width of the vessel. Lightly loaded draft is the minimum vessel draft for stability purposes, from which vertical clearance requirements, such as clearance under bridges, can be determined. <br/><br/>Trim is generally defined as the longitudinal inclination of a ship, or the difference in draught from the bow to the stern. It is controlled by loading. In general, at low speed, a ship underway will squat by the bow. The practice is to counteract this squat by trimming the ship by the stern when loading. The rule of thumb is to provide an allowance of 0.31 m to account for trim in waterway design. The normal approach for a vessel is to assume a trim rate of 3&#8243;/100 ft of length or 0.25 m/100 m. for PTP for maximum vessel size of 440m, 1m is use. <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>Monitoring speed  <br/><br/>  <br/><br/>Ship performance is measured through different method that range from Non-liner motions functions of equipments, stresses and impacts, Inertial forces and Damage to equipments, and speed reduction.  <br/><br/>  <br/><br/>  <br/><br/>Ship motions can be investigated in 4 different ways: <br/><br/>  <br/><br/>  <br/><br/>Theoretical investigations –     Derive simple analytical expressions for describing surface of the seaway and determine the ensuing vessel motions. <br/><br/>  <br/><br/>The studies include the following: <br/><br/>  <br/><br/>-         Important characteristics of the vessel and the environment  <br/><br/>-         Prediction of motions <br/><br/>-         Insight into acceptable values of motions <br/><br/>-         Knowledge of average performance to be expected including stability and resistance <br/><br/>-         Basic ideas regarding motions stabilization and ways to achieve it <br/><br/>-         Guidelines for model tests and full-scale trials <br/><br/>  <br/><br/>However, since ship motions are highly complex, a combination of ways has to be used. <br/><br/>  <br/><br/>In conjunction with theory, experiments are carried out to predict ship performance and  ship trials are conducted in order to correlate model and ship results.   <br/><br/>   <br/><br/>Computer simulations are also used to study the ship performance.  This is usually in the areas where complex behavior as non-linear cannot be predicted analytically and performed experimentally.   <br/><br/>  <br/><br/>  <br/><br/>The degree of irregularity of a seaway can be shown by the shape of its Histogram. <br/><br/>  <br/><br/>         i.e. Frequency of occurrence for the individual wave characteristics. <br/><br/>  <br/><br/>Histogram is basically derived from the record of wave elevations as shown: <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>Also, another way of plotting the Histogram is to plot the cumulative distribution as by diagram below: <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>It has been found by experience that the theoretical Rayleigh curve fits the histograms for the wave height (double amplitude) very well.  Further discussions on this subject will be mentioned later. <br/><br/>  <br/><br/>  <br/><br/>Vessel Motions in Irregular Seaway <br/><br/>  <br/><br/>Though the principal of linear superposition has to be adhered to, it has been found from experiments that the response of ships in irregular seas indicated that the linear spectral techniques yielded unexpectedly accurate results in seas as high as seastate 7. <br/><br/>  <br/><br/>Thus, practically linear theory can be applied for up to moderate sea state cases. <br/><br/>  <br/><br/>The basic steps in predicting the vessel motions are given as follow: <br/><br/>  <br/><br/>1.                  Choose a suitable wave spectrum S(w) <br/><br/>  <br/><br/>2.                  Calculate the encounter frequency wE, as a function of the wave frequency w, vessel speed V, wave speed e, and heading m: wE = w(1 – V.c-1 cos m) <br/><br/>[m = o0 for following seas, 180o for head seas] <br/><br/>  <br/><br/>3.                  Calculate the encounter spectrum S(wE) = S(w) x dw/dwE <br/><br/>  <br/><br/>4.                  Evaluate R.A.O =  <br/><br/>  <br/><br/>Where it is assumed that; <br/><br/>  <br/><br/>(a)    The response to each component wave is independent of the response to the other waves. <br/><br/>  <br/><br/>(b)   The response is a linear function of the component wave amplitudes. <br/><br/>  <br/><br/>[ * a commonly used wave input parameter is the wave amplitude for           translational motions or wave slope for rotational motions ] <br/><br/>  <br/><br/>  <br/><br/>5.                  Plot the response spectrum SR(wE) = S(wE) x (R.A.O)2 <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>The frictional resistance of the large, full bodied ships will very easily be changed in the course of time because of fouling. In practice, the increase of resistance caused by heavy weather depends on the current, the wind, as well as the wave size, where the latter factor may have great influence. Thus, if the wave size is relatively high, the ship speed will be somewhat reduced even when sailing in fair seas. <br/><br/>  <br/><br/>  <br/><br/>Because waves are highly variable within a specified sea state, it is prudent for final design to perform parametric studies for similar ships and, in many cases, to conduct studies to develop realistic estimates. Such studies could consider:  <br/><br/>  <br/><br/>(a) Analytic studies, using strip theory or other theoretical calculation methods as developed by naval architects.  <br/><br/>(b) Interactive, real-time ship simulator studies. <br/><br/>(c) Physical model studies, using radio-controlled, free-running scaled ship models with wave response measurements. <br/><br/>(d) Direct, onboard ship measurements while transiting through the entrance channel. <br/><br/>  <br/><br/>Physical model studies to aid in probabilistic navigation channel design are also used for evaluation. Direct field measurements of ship motion are valuable additional studies, but extreme conditions controlling design are not easily captured. Field measurements are dependent on available ships and environmental conditions during the limited duration of the measurement program. (Wang et al. 1980).  <br/><br/>  <br/><br/>Exxon International Company published a report based on Empirically Method for Estimating Vertical Ship Excursions in Waves.entitles “Underkeel Clearance in Ports” in 1982. outlined a  procedure to estimate the allowance required for a tanker due to wave-induced motions, Based on the model tests conducted at the Netherlands Ship Model Basin (NSMB) (Koele and Hooft 1969) .the responses of a loaded, untrimmed 200K dwt tanker in shallow-water waves were estimated. The majority of the tests were conducted with ship speeds of 7 knots. Based on SOREAH model tests (1973a-c) and some theoretical predictions for a 21K dwt tanker performed by NSMB (1980), Kimon (1982) extrapolated the 200K dwt tanker responses and other vessel sizes.  <br/><br/>  <br/><br/> Deep-water wave data can be used to determine general trends in wave characteristics for the project area, but complexities in local bathymetry and shore orientation will produce a local wave climate that is different from the offshore data. The effects of the direction of water currents ebb and flood tidal currents, on the waves must also be taken into account in determining the characteristics of the waves being encountered by the ship in an entrance channel. It is important that wave characteristics represent the waves that the ship will encounter since the motions of the ship are the result of the ship’s response to the waves. <br/><br/>  <br/><br/>Predicting ship response in wave is a major problem without easy solution. Physical models can be used to predict ship response from monochromatic waves, if model ships are properly scaled, constructed, balanced, instrumented, and tested, lack of data results in difficulty in verifying proposed models to predict the motion of a ship induced by waves to compensate for this motion. <br/><br/>  <br/><br/>  <br/><br/> Speed deterioration as hull deteriorate <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>  <br/><br/>Computer program for time-and-motion simulations which applies predicted tides and tidal currents, historical or projected ship cargoes, drafts, and arrival times at the ocean entrance, and cargo transfer rates at port can also be used. The same model can simulate ship transit times with various dredged channel geometries. Waiting times are computed as the difference between transit time simulated across the shoals and transit time without shoal restrictions. Deeper channels will tend to be more efficient sediment traps and can shoal at faster rates (Trawle 1981). However, a deeper channel might tend to localize shoaling and could reduce the length of channel to be dredged and cost of maintenance dredging <br/><br/>  <br/><br/>Randomly occurring combinations of variables affecting transit times, such as strong winds, river discharge- and wind-induced depth changes, high waves, low visibility, and ice conditions can be added using a Monte Carlo approach. This method requires enough repeated simulations of the same input variables with random values of stochastic variables to encounter the full range of combined extremes. Statistics of transit time, waiting time, and associated costs can be computed from these data. A more complete discussion of vessel traffic flow simulation models is given by PIANC (1997a). <br/><br/>  <br/><br/>Ship costs are generally proportional to operating time, either under way or at berth. Reductions in time navigating the port approach, at the dock, and departing translate into cost savings. Other cost factors include impacts of ship arrivals on longshoremen, mechanical equipment, and cargo staging at the port. Transportation costs without channel improvement must be estimated as a baseline against which to measure cost-effective optimization of channel excavation. The savings realized by a range of excavation depths and channel configurations should be compared with corresponding dredging and disposal costs. The ideal optimum will achieve the maximum net savings, but environmental quality effects, financial capabilities, and user preferences can affect the final project design.  <br/><br/></p>


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		<title>quantum art and poetry: An objective existence for the wave &#8230;</title>
		<link>http://wave-mechanics.materialgeek.com/quantum-art-and-poetry-an-objective-existence-for-the-wave/</link>
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		<pubDate>Tue, 01 Jun 2010 14:30:00 +0000</pubDate>
		<dc:creator>Material Geek</dc:creator>
				<category><![CDATA[Wave Mechanics]]></category>
		<category><![CDATA[Collapsing And]]></category>
		<category><![CDATA[Continuously Collapsing]]></category>
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		<description><![CDATA[In this theory on quantum mechanics the quantum wave particle function continuously collapsing and reforming forms the forward passage of time. Therefore Heisenberg Uncertainty Principle that is formed by the wave function is the same ...


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			<content:encoded><![CDATA[<p>In this theory on quantum mechanics the quantum wave particle function continuously collapsing and reforming forms the forward passage of time. Therefore Heisenberg Uncertainty Principle that is formed by the wave function is the same &#8230;</p>
<p><span id="more-494"></span></p>
<p>Read more from the original source:<br />
<a target="_blank" href="http://quantumartandpoetry.blogspot.com/2010/06/objective-existence-for-wave-function.html" title="quantum art and poetry: An objective existence for the wave ...">quantum art and poetry: An objective existence for the wave &#8230;</a></p>
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<li><a href='http://wave-mechanics.materialgeek.com/albert-einstein-%c2%bb-wave-function-and-wave-particle-duality/' rel='bookmark' title='Permanent Link: Albert Einstein » Wave Function And Wave-Particle Duality'>Albert Einstein » Wave Function And Wave-Particle Duality</a></li>
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</ol></p>]]></content:encoded>
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		<title>Popular Mechanics iPad App: The Future of Magazines, All Over &#8230;</title>
		<link>http://wave-mechanics.materialgeek.com/popular-mechanics-ipad-app-the-future-of-magazines-all-over/</link>
		<comments>http://wave-mechanics.materialgeek.com/popular-mechanics-ipad-app-the-future-of-magazines-all-over/#comments</comments>
		<pubDate>Tue, 01 Jun 2010 13:10:15 +0000</pubDate>
		<dc:creator>Material Geek</dc:creator>
				<category><![CDATA[Wave Mechanics]]></category>
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		<description><![CDATA[The Great iPad Magazine isn't here yet—but it's getting closer all the time. Popular Mechanics ' app, set to launch next month, already looks like th... 


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			<content:encoded><![CDATA[<p>The Great iPad Magazine isn&#8217;t here yet—but it&#8217;s getting closer all the time. Popular Mechanics &#8216; app, set to launch next month, already looks like th&#8230; </p>
<p><span id="more-492"></span></p>
<p>Read more here:<br />
<a target="_blank" href="http://blog.olebox.com/2010/06/01/popular-mechanics-ipad-app-the-future-of-magazines-all-over-again-ipad-apps/" title="Popular Mechanics iPad App: The Future of Magazines, All Over ...">Popular Mechanics iPad App: The Future of Magazines, All Over &#8230;</a></p>
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		<title>Texas Firm Wins Approval for Wave-Powered Desalination Plant</title>
		<link>http://wave-mechanics.materialgeek.com/texas-firm-wins-approval-for-wave-powered-desalination-plant/</link>
		<comments>http://wave-mechanics.materialgeek.com/texas-firm-wins-approval-for-wave-powered-desalination-plant/#comments</comments>
		<pubDate>Tue, 01 Jun 2010 13:00:00 +0000</pubDate>
		<dc:creator>Material Geek</dc:creator>
				<category><![CDATA[Wave Mechanics]]></category>
		<category><![CDATA[A Marketing Project]]></category>
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		<description><![CDATA["I don't want to make bottled water a revenue stream," RBI founder and CEO Mark Thomas told Popular Mechanics last year. "[F]or the most part, it's a marketing project. I want to have a tangible, portable product made entirely from wave ...


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			<content:encoded><![CDATA[<p>&#8220;I don&#8217;t want to make bottled water a revenue stream,&#8221; RBI founder and CEO Mark Thomas told Popular Mechanics last year. &#8220;[F]or the most part, it&#8217;s a marketing project. I want to have a tangible, portable product made entirely from wave &#8230;</p>
<p><span id="more-493"></span></p>
<p>Originally posted here:<br />
<a target="_blank" href="http://theenergycollective.com/TheEnergyCollective/67146" title="Texas Firm Wins Approval for Wave-Powered Desalination Plant">Texas Firm Wins Approval for Wave-Powered Desalination Plant</a></p>
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		<title>SYLLABUS FOR IIT</title>
		<link>http://wave-mechanics.materialgeek.com/syllabus-for-iit/</link>
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		<pubDate>Tue, 01 Jun 2010 10:29:34 +0000</pubDate>
		<dc:creator>Material Geek</dc:creator>
				<category><![CDATA[Articles]]></category>
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		<description><![CDATA[CHEMISTRY SYLLABUS Physical chemistry General topics: Concept of atoms and molecules; Dalton&#8217;s atomic theory; Mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept) involving common oxidation-reduction, neutralisation, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality.Gaseous and liquid states: Absolute scale of temperature, ideal gas equation; Deviation from [...]


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			<content:encoded><![CDATA[<p>CHEMISTRY SYLLABUS <br/><br/>Physical chemistry General topics: Concept of atoms and molecules; Dalton&#8217;s atomic theory; Mole concept; Chemical formulae; Balanced chemical equations; Calculations (based on mole concept) involving common oxidation-reduction, neutralisation, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality.Gaseous and liquid states: Absolute scale of temperature, ideal gas equation; Deviation from ideality, van der Waals equation; Kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature; Law of partial pressures; Vapour pressure; Diffusion of gases.Atomic structure and chemical bonding: Bohr model, spectrum of hydrogen atom, quantum numbers; Wave-particle dualiy, de Broglie hypothesis; Uncertainty principle; Qualitative quantum mechanical picture of hydrogen atom, shapes of s, p and d orbitals; Electronic configurations of elements (up to atomic number 36); Aufbau principle; Pauli&#8217;s exclusion principle and Hund&#8217;s rule; Orbital overlap and covalent bond; Hybridisation involving s, p and d orbitals only; Orbital energy diagrams for homonuclear diatomic species; Hydrogen bond; Polarity in molecules, dipole moment (qualitative aspects only); VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral and octahedral).Energetics: First law of thermodynamics; Internal energy, work and heat, pressure-volume work; Enthalpy, Hess&#8217;s law; Heat of reaction, fusion and vapourization; Second law of thermodynamics; Entropy; Free energy; Criterion of spontaneity. Chemical equilibrium: Law of mass action; Equilibrium constant, Le Chatelier&#8217;s principle (effect of concentration, temperature and pressure); Significance of DG and DGo in chemical equilibrium; Solubility product, common ion effect, pH and buffer solutions; Acids and bases (Bronsted and Lewis concepts); Hydrolysis of salts. Electrochemistry: Electrochemical cells and cell reactions; Standard electrode potentials; Nernst equation and its relation to DG; Electrochemical series, emf of galvanic cells; Faraday&#8217;s laws of electrolysis; Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch&#8217;s law; Concentration cells. Chemical kinetics: Rates of chemical reactions; Order of reactions; Rate constant; First order reactions; Temperature dependence of rate constant (Arrhenius equation). Solid state: Classification of solids, crystalline state, seven crystal systems (cell parameters a, b, c, alpha, beta, gamma), close packed structure of solids (cubic), packing in fcc, bcc and hcp lattices; Nearest neighbours, ionic radii, simple ionic compounds, point defects. Solutions: Raoult&#8217;s law; Molecular weight determination from lowering of vapour pressure, elevation of boiling point and depression of freezing point. Surface chemistry: Elementary concepts of adsorption (excluding adsorption isotherms); Colloids: types, methods of preparation and general properties; Elementary ideas of emulsions, surfactants and micelles (only definitions and examples). Nuclear chemistry: Radioactivity: isotopes and isobars; Properties of alpha, beta and gamma rays; Kinetics of radioactive decay (decay series excluded), carbon dating; Stability of nuclei with respect to proton-neutron ratio; Brief discussion on fission and fusion reactions. Inorganic Chemistry Isolation/preparation and properties of the following non-metals: Boron, silicon, nitrogen, phosphorus, oxygen, sulphur and halogens; Properties of allotropes of carbon (only diamond and graphite), phosphorus and sulphur.Preparation and properties of the following compounds: Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium, potassium, magnesium and calcium; Boron: diborane, boric acid and borax; Aluminium: alumina, aluminium chloride and alums; Carbon: oxides and oxyacid (carbonic acid); Silicon: silicones, silicates and silicon carbide; Nitrogen: oxides, oxyacids and ammonia; Phosphorus: oxides, oxyacids (phosphorus acid, phosphoric acid) and phosphine; Oxygen: ozone and hydrogen peroxide; Sulphur: hydrogen sulphide, oxides, sulphurous acid, sulphuric acid and sodium thiosulphate; Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder; Xenon fluorides.Transition elements (3d series): Definition, general characteristics, oxidation states and their stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic moment; Coordination compounds: nomenclature of mononuclear coordination compounds, cis-trans and ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar and octahedral).Preparation and properties of the following compounds: Oxides and chlorides of tin and lead; Oxides, chlorides and sulphates of Fe2+, Cu2+ and Zn2+; Potassium permanganate, potassium dichromate, silver oxide, silver nitrate, silver thiosulphate. Ores and minerals:Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminium, zinc and silver. Extractive metallurgy: Chemical principles and reactions only (industrial details excluded); Carbon reduction method (iron and tin); Self reduction method (copper and lead); Electrolytic reduction method (magnesium and aluminium); Cyanide process (silver and gold). Principles of qualitative analysis: Groups I to V (only Ag+, Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+); Nitrate, halides (excluding fluoride), sulphate and sulphide. <br/><br/>Organic Chemistry   <br/><br/>Concepts: Hybridisation of carbon; Sigma and pi-bonds; Shapes of simple organic molecules; Structural and geometrical isomerism; Optical isomerism of compounds containing up to two asymmetric centres, (R,S and E,Z nomenclature excluded); IUPAC nomenclature of simple organic compounds (only hydrocarbons, mono-functional and bi-functional compounds); Conformations of ethane and butane (Newman projections); Resonance and hyperconjugation; Keto-enol tautomerism; Determination of empirical and molecular formulae of simple compounds (only combustion method); Hydrogen bonds: definition and their effects on physical properties of alcohols and carboxylic acids; Inductive and resonance effects on acidity and basicity of organic acids and bases; Polarity and inductive effects in alkyl halides; Reactive intermediates produced during homolytic and heterolytic bond cleavage; Formation, structure and stability of carbocations, carbanions and free radicals. Preparation, properties and reactions of alkanes: Homologous series, physical properties of alkanes (melting points, boiling points and density); Combustion and halogenation of alkanes; Preparation of alkanes by Wurtz reaction and decarboxylation reactions. Preparation, properties and reactions of alkenes and alkynes: Physical properties of alkenes and alkynes (boiling points, density and dipole moments); Acidity of alkynes; Acid catalysed hydration of alkenes and alkynes (excluding the stereochemistry of addition and elimination); Reactions of alkenes with KMnO4 and ozone; Reduction of alkenes and alkynes; Preparation of alkenes and alkynes by elimination reactions; Electrophilic addition reactions of alkenes with X2, HX, HOX and H2O (X=halogen); Addition reactions of alkynes; Metal acetylides. Reactions of benzene: Structure and aromaticity; Electrophilic substitution reactions: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation; Effect of o-, m- and p-directing groups in monosubstituted benzenes. Phenols: Acidity, electrophilic substitution reactions (halogenation, nitration and sulphonation); Reimer-Tieman reaction, Kolbe reaction. Characteristic reactions of the following (including those mentioned above): Alkyl halides: rearrangement reactions of alkyl carbocation, Grignard reactions, nucleophilic substitution reactions; Alcohols: esterification, dehydration and oxidation, reaction with sodium, phosphorus halides, ZnCl2/concentrated HCl, conversion of alcohols into aldehydes and ketones; Ethers:Preparation by Williamson&#8217;s Synthesis; Aldehydes and Ketones: oxidation, reduction, oxime and hydrazone formation; aldol condensation, Perkin reaction; Cannizzaro reaction; haloform reaction and nucleophilic addition reactions (Grignard addition); Carboxylic acids: formation of esters, acid chlorides and amides, ester hydrolysis; Amines: basicity of substituted anilines and aliphatic amines, preparation from nitro compounds, reaction with nitrous acid, azo coupling reaction of diazonium salts of aromatic amines, Sandmeyer and related reactions of diazonium salts; carbylamine reaction; Haloarenes: nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine substitution). Carbohydrates: Classification; mono- and di-saccharides (glucose and sucrose); Oxidation, reduction, glycoside formation and hydrolysis of sucrose. Amino acids and peptides: General structure (only primary structure for peptides) and physical properties. Properties and uses of some important polymers: Natural rubber, cellulose, nylon, teflon and PVC. Practical organic chemistry: Detection of elements (N, S, halogens); Detection and identification of the following functional groups: hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, amino and nitro; Chemical methods of separation of mono-functional organic compounds from binary mixtures. <br/><br/>PHYSICS SYLLABUS <br/><br/>General: Units and dimensions, dimensional analysis; least count, significant figures; Methods of measurement and error analysis for physical quantities pertaining to the following experiments: Experiments based on using Vernier calipers and screw gauge (micrometer), Determination of g using simple pendulum, Young&#8217; modulus by Searle&#8217;s method, Specific heat of a liquid using calorimeter, focal length of a concave mirror and a convex lens using u-v method, Speed of sound using resonance column, Verification of Ohm&#8217; law using voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post office box. Mechanics: Kinematics in one and two dimensions (Cartesian coordinates only), projectiles; Uniform Circular motion; Relative velocity. Newton&#8217;s laws of motion; Inertial and uniformly accelerated frames of reference; Static and dynamic friction; Kinetic and potential energy; Work and power; Conservation of linear momentum and mechanical energy. Systems of particles; Centre of mass and its motion; Impulse; Elastic and inelastic collisions.Law of gravitation; Gravitational potential and field; Acceleration due to gravity; Motion of planets and satellites in circular orbits; Escape velocity. Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of inertia of uniform bodies with simple geometrical shapes; Angular momentum; Torque; Conservation of angular momentum; Dynamics of rigid bodies with fixed axis of rotation; Rolling without slipping of rings, cylinders and spheres; Equilibrium of rigid bodies; Collision of point masses with rigid bodies. Linear and angular simple harmonic motions. Hooke&#8217;s law, Young&#8217; modulus. Pressure in a fluid; Pascal&#8217;s law; Buoyancy; Surface energy and surface tension, capillary rise; Viscosity (Poiseuille&#8217;s equation excluded), Stoke&#8217;s law; Terminal velocity, Streamline flow, equation of continuity, Bernoulli&#8217;s theorem and its applications. Wave motion (plane waves only), longitudinal and transverse waves, superposition of waves; Progressive and stationary waves; Vibration of strings and air columns;Resonance; Beats; Speed of sound in gases; Doppler effect (in sound). Thermal physics: Thermal expansion of solids, liquids and gases; Calorimetry, latent heat; Heat conduction in one dimension; Elementary concepts of convection and radiation; Newton&#8217;s law of cooling; Ideal gas laws; Specific heats (Cv and Cp for monoatomic and diatomic gases); Isothermal and adiabatic processes, bulk modulus of gases; Equivalence of heat and work; First law of thermodynamics and its applications (only for ideal gases); Blackbody radiation: absorptive and emissive powers; Kirchhoff&#8217;s law; Wien&#8217;s displacement law, Stefan&#8217;s law. Electricity and magnetism: Coulomb&#8217;s law; Electric field and potential; Electrical potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field; Electric field lines; Flux of electric field; Gauss&#8217;s law and its application in simple cases, such as, to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Capacitance; Parallel plate capacitor with and without dielectrics; Capacitors in series and parallel; Energy stored in a capacitor. Electric current; Ohm&#8217;s law; Series and parallel arrangements of resistances and cells; Kirchhoff&#8217;s laws and simple applications; Heating effect of current. Biot-avart&#8217;s law and Ampere&#8217;s law; Magnetic field near a current-carrying straight wire, along the axis of a circular coil and inside a long straight solenoid; Force on a moving charge and on a current-carrying wire in a uniform magnetic field. Magnetic moment of a current loop; Effect of a uniform magnetic field on a current loop; Moving coil galvanometer, voltmeter, ammeter and their conversions. Electromagnetic induction: Faraday&#8217;s law, Lenz&#8217;s law; Self and mutual inductance; RC, LR and LC circuits with d.c. and a.c. sources. Optics: Rectilinear propagation of light; Reflection and refraction at plane and spherical surfaces; Total internal reflection; Deviation and dispersion of light by a prism; Thin lenses; Combinations of mirrors and thin lenses; Magnification. Wave nature of light: Huygen&#8217;s principle, interference limited to Young&#8217;s double-slit experiment.Modern physics: Atomic nucleus; Alpha, beta and gamma radiations; Law of radioactive decay; Decay constant; Half-life and mean life; Binding energy and its calculation; Fission and fusion processes; Energy calculation in these processes. Photoelectric effect; Bohr&#8217;s theory of hydrogen-like atoms; Characteristic and continuous X-rays, Moseley&#8217;s law; de Broglie wavelength of matter waves. <br/><br/>MATHEMATICS SYLLABUS  <br/><br/>Algebra: Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.Logarithms and their properties. Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.Trigonometry: Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only).Analytical geometry: Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.Equation of a straight line in various forms, angle between two lines, distance of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle.Equation of a circle in various forms, equations of tangent, normal and chord.Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal. Locus Problems.Three dimensions: Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.Differential calculus: Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L&#8217;Hospital rule of evaluation of limits of functions.Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions.Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, Rolle&#8217;s Theorem and Lagrange&#8217;s Mean Value Theorem.Integral calculus: Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, Fundamental Theorem of Integral Calculus.Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves.Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations.Vectors: Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical interpretations. <br/><br/>  <br/><br/><span id="more-488"></span>
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