Theoretical Solid State Physics

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Theoretical Perspectives of Spin Dynamics in Solid State Nuclear Magnetic Resonance and Physics

Theoretical Perspectives of Spin Dynamics in Solid State Nuclear Magnetic Resonance and Physics

DOI: 10.4236/jmp.2018.98103 1650 Journal of Modern Physics the physical meaning of the FME can be found in the literature. The connection between the Magnus expansion and the Floquet theory was established in the FME [24]. The FME approach is an alternative approach recently developed by Casas and co-workers to solve time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state nuclear mag- netic resonance (SSNMR) in particular [24]. The authors Casas, Oteo, and Ros build up a recursive scheme to obtain the terms in the new expansion and give an explicit sufficient condition for its convergence. The method and formulae were applied to an illustrative example from nuclear magnetic resonance, quan- tum mechanics, and physics [11]. When making the connection between the time-ordered products and the Magnus expansion, Oteo and Ros mentioned that the initial value problem originated from the linear homogeneous ordinary differential equation (LHODE) of first order [45]. The LHODE plays a pervasive role in many branches of mathematics, physics, and engineering with a wide range of different mathematical and physical meanings for the variable involved. Theoretical problems in solid-state NMR are widely treated with the average Hamiltonian theory and the Floquet theory. A variety of magnetic resonance phenomena has been described using both theories (AHT and FLT). These theo- ries have been successful for designing sophisticated pulse sequences and under- standing of different experiments. For instance, recently, the AHT has been used to develop a set of selection rules based on the symmetry of the internal interac- tions and Euler angles in order to simplify the design of NMR multiple-pulse sequences in the presence of sample rotation. This allows the development of recoupling and decoupling sequences as well as many other experiments. The selection rules reveal which types of interactions can be recoupled by a sequence with a given symmetry. Similarly, the FLT has been used to describe multipho- ton effects in NMR, electron paramagnetic resonance, and nuclear quadrupole resonance. The fusion of AHT and FLT is generalized by the Floquet-Magnus expansion [1] [9] [24] [46] [47] [48] [49] [50]. The FME has been recently ap- plied to various problems in solid-state NMR and Physics [51] [52] [53] [54] [55].
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Two Theoretical Approaches in Solid State Nuclear Magnetic Resonance Spectroscopy

Two Theoretical Approaches in Solid State Nuclear Magnetic Resonance Spectroscopy

This new method provides a useful alternative to the exponential mapping relating the Lie algebra to the Lie group. This fact is particularly important for numerical methods where the evaluation of the exponential matrix is the most computation-intensive part of the algorithm. It is noteworthy that the combinations of two or more of the theories known in NMR will continue to provide a framework for treating time-dependent Hamiltonian in quantum physics and NMR in a more efficient way that can be easily extended to all types of modulations.

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Economics and Theoretical Physics

Economics and Theoretical Physics

to arrive at the theory of the ``quas-irigid'' luminiferous ether, the parts of which can carry out no movements relatively to one another except the small movements of deformation which correspond to light-waves. ” 11 The evidence of this fabric which may be in a solid state may become evident when the refresh rate (number of pages flipped) of matter either increases or falls which creates a resistance or field effect we refer to as gravity, mass etc. Since, as explained, the source of Newtonian forces, including inertia, when understood at the operational level are created by neither velocity nor acceleration then we need to search for other unifying sources or causes for forces evident in weight, mass, gravity and inertia. .” As the cartoonist flips each page to generate a moving vehicle there may be a transfer of kinetic energy that manifests itself to the observer as a wave, movement and as mass, which is why, even objects with “no velocity” relative to other objects that are, for example, as large as the Earth create a gravitational field. In other words though they are “standing still”, the fact their standing still continues to be generated by the “ cartoonist flipping pages ” (the refresh or frame rate of matter) causes a gravitational field effect rather than the displacement of Space-Time proposed by Einstein. The process of refreshing cannot strictly be described as a vibration such as the example of a guitar string used to describe String Theory for one simple reason; this type of vibration does not accommodate the disappearance and reappearance of matter when it refreshes. It is possible that it is the nature of this transference or kinetic energy that is creating mass rather than the movement of the image since in reality or at the operating level its velocity (on each page or frame) is always zero. Using this logic a wrecking ball knocking down a wall does not gain the energy with which it knocks down the wall from its momentum, since its speed and velocity are always zero. It is gaining this weight, gravity or force which knocks down the wall from some other phenomenon taking place behind the scenes. Remember earlier we estimated that matter refreshes 90 billion times “per second”, 90 billion is representative of C 2 in Einstein’s E=M C 2 . Light may refresh at a rate of C 2 and therefore appear to weigh
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Experimental and Theoretical Physics Work on Plutonium Enriched LWR's Lattices  EUR 4434

Experimental and Theoretical Physics Work on Plutonium Enriched LWR's Lattices EUR 4434

two types of holes in the grids : ­ the first type allows to load the fuel pins with a square pitch of 1.303 cm equal to the fuel pitch in the ¿ήΝΑ assemblies square pitches of /2 χ 1.30[r]

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Solid Propellant Motor Design: Comparison of Theoretical and Experimental Data

Solid Propellant Motor Design: Comparison of Theoretical and Experimental Data

solid rocket was to carry the ballistic rocket and payload to an altitude at range 100 to 200 m. To meet this requirement, the solid propellant rocket motor to be developed. The process included designing, analysis and construction of the motor. In designing the motor, a propellant formulation was used from various source and initially verified to find the best compounds. This formulation was then used to determine the interior ballistic properties and grain geometry that allow the motor complete the mission. Then, all component of the motor including case, nozzle and the actual propellant segments had to fabricate.
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Geometrical and topological foundations of theoretical physics: from gauge theories to string program

Geometrical and topological foundations of theoretical physics: from gauge theories to string program

3. Introduction to Kaluza-Klein theories. In another direction, there have been in the 1920s very interesting attempts by Theodor Kaluza then by Oskar Klein to unify the relativistic theory of gravitation with Maxwell’s theory by introducing a new geo- metrical framework within which electromagnetism could be coupled with gravity (at least theoretically). The Kaluza-Klein theories are purely geometrical in character and have been worked out in order to encompass two apparently inconsistent physical the- ories into a unitary theoretical explanation. Actually, even before Einstein’s general relativity, the physicist Gunnar Nordström in 1914 proceeded to unify his theory of gravitation (in which gravity was described by a scalar field coupled with the trace of the energy momentum tensor) with Maxwell’s theory in a most imaginative way. In- spired by Minkowski’s four-dimensional spacetime continuum, Nordström added yet another space dimension, thus obtaining a flat five-dimensional world. There he intro- duced an Abelian five-vector gauge field for which he wrote down the Maxwell equations including a conserved five-current. He then identified the fifth component of the five- vector potential with scalar gravity, whereas he identified the first four components of the five-vector potential with the Maxwell four-potential. With these interpretations he then noticed that in the cylindrical case (when all dynamical variables become inde- pendent of the fifth coordinate) the equations of his five-dimensional Maxwell theory reduced to those of the four-dimensional Maxwell-Nordström electromagnetic gravi- tational theory. It is then fair to say that higher-dimensional unification starts with Nordström, who assumed scalar gravity in our four-dimensional world to be a remnant of an Abelian gauge theory in a five-dimensional flat spacetime.
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Prediction of NMR parameters in the solid-state

Prediction of NMR parameters in the solid-state

The electrons in an atom can be divided into two types — core electrons and valence electrons. The core elec- trons are tightly bound to the nucleus, while the valence electrons are more extended. A working definition for core electrons is that they are the ones which play no part in the interactions between atoms, while the valence elec- trons dictate most of the properties of the material. It is common to make the frozen core approximation. The core electrons are constrained not to differ from their free atomic nature when placed in the solid state envi- ronment. This reduces the number of electronic degrees of freedom in an all electron calculation. It is a very good approximation. A different, but physically related, approach is taken in the pseudopotential approximation. Since, in an all electron calculation, the valence elec- tron wavefunctions must be orthogonal to the core wave- functions they necessarily have strong oscillations in the region near the nucleus (see the all electron wavefunction in Figure 3). Given that a planewave basis set is to be used to describe the wavefunctions, these strong oscilla- tions are undesirable — requiring many plane waves for an accurate description. Further, these oscillations are of very little consequence for the electronic structure in the solid, since they occur close to the nucleus, and interact little with the neighboring atoms. In the pseudopotential approach only the valence electrons are explicitly consid- ered, the effects of the core electrons being integrated within a new ionic potential. The valence wavefunctions need no longer be orthogonal to the core states, and so the orthogonality oscillations disappear, hence far fewer plane waves are required to describe the valence wave- functions.
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Efficient Theoretical Screening of Solid Sorbents for CO2 Capture Applications

Efficient Theoretical Screening of Solid Sorbents for CO2 Capture Applications

3.1. Applications to Alkali and Alkaline Earth Metal Oxides and Hydroxides [4,12-14] The thermodynamic data for these oxides, hydroxides and corresponding carbonates and bicarbonates are avai- lable in thermodynamic databases, in order to validate our theoretical approach, we also made the ab initio ther- modynamic calculations for these known crystals. Table 1 shows the calculated thermodynamic properties of these reactions accompanying with experimental data obtained from HSC Chemistry database [27].

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A solid-state atomic frequency standard

A solid-state atomic frequency standard

This thesis describes a new class of frequency reference. The frequency source uses the same operating principle as a passive atomic frequency standard; however, the device is entirely solid-state, removing many cost and reliability issues associated with gas-phase atomic clocks. The basis for the solid-state atomic frequency standard is the zero-field electron magnetic resonance of certain transition metal ions doped into dielectric crystals. As Chapters 2 and 3 will describe, the divalent vanadium ion in magnesium oxide has a narrow magnetic resonance spectrum at room temperature. The features of the zero-field magnetic resonance spectra are discussed in detail. Magnesium oxide is a common ceramic, and may be manufactured at very low cost. An important feature of the solid-state atomic frequency standard is that the reference frequency is accuracy defined by the materials system, rather than depending acutely on the manufacturing tolerances as is the case for crystal oscillators.
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Solid State Transformers: The State-of-the-Art, Challenges and Applications

Solid State Transformers: The State-of-the-Art, Challenges and Applications

In the previous years, SST has received the attention off different academic and industrial sectors regarding its applications and benefits. This paper reviewed, generally, the state of art of SST, form the available topologies, HV SST to its efficiency in recent ways. In addition, the applications of SST are well explained to check and identify where and how the SST could work in different electric sections. It has been evident that using the SST in the distribution system could help in achieving the required smart grid. The paper also summarizes the most important challenges that are facing the applications of SST in the system and it shows that the most important development in SST will be evident with the development of the new generation of power electronic semiconductor.
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Physics of the charmonium-like state X(3872)

Physics of the charmonium-like state X(3872)

The solid line is our theoret- ical one with taking into account the Belle energy resolution.. The dotted line is a square root function for the incoherent background..[r]

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Instructional Needs Assessment of Physics Teachers in the Teaching of Physics and Physics Practical in Ogun State Secondary Schools, Nigeria

Instructional Needs Assessment of Physics Teachers in the Teaching of Physics and Physics Practical in Ogun State Secondary Schools, Nigeria

123 | P a g e The result in Table 2 revealed a non-significant outcome (t=0.17, p> 0.05). This outcome implies that the sampled physics teachers’ instructional needs did not significantly differ with respect to their experience. The mean score of more experienced physics teachers (53.67) is higher than that of less experienced teachers (53.63), but the difference is not statistically significant. Hence, hypothesis 2 (H 0 2), was not rejected. By implication, there is no significant difference between the perceived instructional needs

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Solid State Lighting: A Summarization of Advancements

Solid State Lighting: A Summarization of Advancements

Our world is rapidly advancing forward, newer technologies are appearing every day and the most simplest of processes are automated. The discovery of the light bulb by Thomas Edison revolutionized the concepts of lighting. The lighting industry has been growing ever since that day. Today, the market has to offer several different kinds of lamps and bulbs. The consumption of electricity is at an all- time high and scientists are looking for alternative and renewable sources of energy. New sources of lighting are also being discovered for more efficient consumption of power. Light sources hold a very important position in the world. Making them more efficient and improving, their performance is a priority nowadays. With Compact Fluorescent Lamps and incandescent lamps already in the market, a unique applied science area is emerging rapidly. This applied science technology is profusely called as solid state lightening (SSL). SSL is proving to be the future of conventional lighting sources. Features like longer lifetime, ability to generate a wider range of colors and superior energy conservation make it the preferable choice for using as a lighting source. Solid-state lighting utilizes the concepts
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New compounds and structures in the solid state

New compounds and structures in the solid state

Downloaded by University of Strathclyde on 03 August 2011 Published on 25 May 2011 on http://pubs.rsc.org | doi:10.1039/C1IC90028E View Online Growth of LaTiO2N by an unusual flux method [r]

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Solid State Characterization of Sodium Eritadenate

Solid State Characterization of Sodium Eritadenate

Knowledge of the solid state is of great importance in the development of a new active pharmaceutical in- gredient, since the solid form often dictates the properties and performance of the drug. In the present study, solid state characteristics of the sodium salt of the candidate cholesterol reducing compound eritadenine, 2(R), 3(R)-dihydroxy-4-(9-adenyl)-butanoic acid, were investigated. The compound was crystallized by slow cooling from water and various aqueous ethanol solutions, at different temperatures. Further, the compound solution was subjected to lyophilization and to high vacuum drying. The resulting solids were screened for polymorphism by micro Raman spectroscopy (λ ex = 830 nm) and the crystallinity was investigated by X-ray
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New compounds and structures in the solid state

New compounds and structures in the solid state

reported, TNU-9. A number of potentially useful new compounds have been identified including new phases for second harmonic generation and a new silico- germanate zeolite that exceeds the state-of-the-art as a catalyst for several indust- rially important processes. In addition to these studies the reports of a two- dimensional ferromagnet or an air- and moisture-stable intermetallic phase that shows a strong resemblance to the host/guest chemistry of zeolites indicate that the structure of the solid state continues to be a source of challenging and interesting chemistry.

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New compounds and structures in the solid state

New compounds and structures in the solid state

ground state does not lead to Jahn–Teller instability. Control of the reaction temperature leads to varying degrees of reduction of the SrFeO 3d phases. These reactions are not simply topotactic but involve rearrangement of the anion sublattice and it is remarkable that these reductions, and re-oxidations, can take place at temperatures as low 120 1C indicative of highly mobile oxide anions which nevertheless do not lead to phase separation or any appreciable loss of crystallinity. Low temperatures have also been used to stabilise unusually low oxidation states in the layered compounds La 4 Ni 3 O 8 and Nd 4 Ni 3 O 8 . 17 These compounds were prepared by heating the n = 3
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New compounds and structures in the solid state

New compounds and structures in the solid state

model for a geometrically-frustrated Kagome lattice. The structure of this compound contains an ordered arrangement of paramagnetic Cu 2+ and dia- magnetic Zn 2+ over the sites of a pyrochlore-like lattice. In the absence of chemical ordering, these cations would form a triangular array but in this new metastable polymorph the complete cation ordering introduces diamagnetic holes into the paramagnetic net and produces a Kagome net populated by the S = 1/2 Cu 2+ cation. Interlayer magnetic interactions appear to be weak and preliminary magnetic measurements suggest that these spins may be condensing to the desired nonmagnetic ground state. 33
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EVALUATION OF SOLID STATE FORMS OF CURCUMINOIDS

EVALUATION OF SOLID STATE FORMS OF CURCUMINOIDS

Curcuminoid on crystallization from isopropanol or upon solvent assisted and neat grinding did not undergo any polymorphic changes. The coexistence of the curcumin, DMC and BDMC in curcuminoids studying their polymorphic behaviour presents an interesting aspect of modifying their properties. The solid- state behaviour of curcuminoids was mainly due to its major constituent curcumin, while DMC and BDMC did not contribute to the overall crystalline properties probably owing to the amorphous nature of DMC or to the low percentage of BDMC in the curcuminoids. The differences in the reported polymorphic forms of curcumin i.e., curcumin forms 1-3 and the patented forms I to VI may be due to variations in the purity of curcumin.
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Management of solid waste in khartoum state

Management of solid waste in khartoum state

is generally collected weekly in residential areas and daily in business sections. Solid waste includes any garbage, refuse and any discarded materials including solid, semi-solid, liquid or contained gaseous material resulting from industrial, , mining and agricultural operations, and from Solid waste has become a global common problem to all countries; whether these countries are advanced or developing. The situation in Sudan is not much different from that in other countries with similar Knowing the sources and types of solid wastes, along with data on the composition and rates of generation, is basic to design and operation of the functional elements associated with the management of solid wastes. The materials that are collected under the term solid wastes include many different substances from vary types of sources. The different types and sources of solid waste are shown in the table 1.1 INTERNATIONAL JOURNAL OF CURRENT RESEARCH
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