It is shown that Schr&#xf6;dinger's equation may be derived from three postulates. The first is a kind
of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from
the canonical equations of particle mechanics by replacing all observables by statistical averages. 
The second is a local conservation law of probability with a probability current which takes the
form of a gradient. The third is a principle of maximal disorder as realized by the requirement of
minimal Fisher information. The rule for calculating expectation values is obtained from a fourth
postulate, the requirement of energy conservation in the mean. The fact that all these basic relations
of quantum theory may be derived from premises which are statistical in character is interpreted as
a strong argument in favor of the statistical interpretation of quantum mechanics. The structures of
quantum theory and classical statistical theories are compared, and some fundamental differences are
identified.

U. Klein

The Statistical Origins of Quantum Mechanics

The principle of inductively coupled plasma (ICP) and perspective of ICP development are reviewed. Multispiral coil ICP (MSC-ICP), which has the advantages of low inductance, high efficiency, and excellent uniformity, is discussed in detail. Applications to thin film processing technologies and the future prospects of ICP are also described.

Tomohiro Okumura

Inductively Coupled Plasma Sources and Applications

The study of the evolution of the conduction band in dense gases and supercritical fluids near
the critical point has been complicated by a lack of precise experimental measurements. Both
photoemission from an electrode immersed in the fluid and field ionization of a molecule doped
into the fluid have been used to probe solvent density effects on the energy of an excess electron as
a function of fluid number density and temperature. In this perspective, we present recent experimental results that show a strong critical point effect on the minimum conduction band energy near
the critical density and temperature of a fluid. We also discuss the recent development of a new
theoretical model that advances our understanding of the density and temperature dependence of
the conduction band minimum in near critical point fluids.

C. M. Evans

G. L. Findley

Energy of the Conduction Band in Near Critical Point Fluids

A finite-time generic model to describe the behavior of real refrigeration systems is discussed. The model accounts for finite heat transfer rates, heat leaks, and friction as different sources of dissipation. The performance characteristics are cast in terms of cooling rate (<svg style="vertical-align:-0.1638pt;width:7.3000002px;" id="M1" height="7.9499998" version="1.1" viewBox="0 0 7.3000002 7.9499998" width="7.3000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D45F" d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26&#xA;q13 -21 0 -43z" /></g></svg>) versus coefficient of performance 
(<svg style="vertical-align:-0.1638pt;width:12.225px;" id="M2" height="7.9499998" version="1.1" viewBox="0 0 12.225 7.9499998" width="12.225" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D464" d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152&#xA;q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" /></g></svg>). For comparison purposes, various types of refrigeration/heat pump systems are considered: the thermoelectric refrigerator, the reverse Brayton cycle, and the reverse Rankine cycle. Although the dissipation mechanisms are different (e.g., heat leak and Joule heating in the thermoelectric refrigerator, isentropic losses in the reverse Brayton cycle, and limits arising from the equation of state in the reverse Rankine cycle), the <svg style="vertical-align:-0.1638pt;width:36.9375px;" id="M3" height="7.9499998" version="1.1" viewBox="0 0 36.9375 7.9499998" width="36.9375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45F" /></g><g transform="matrix(.017,-0,0,-.017,11.01,7.675)"><path id="x2212" d="M535 230h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,24.762,7.675)"><use xlink:href="#x1D464" /></g></svg> characteristic curves have a general loop shape. There are four limiting types of operation: open circuit in which both <svg style="vertical-align:-0.1638pt;width:7.3000002px;" id="M4" height="7.9499998" version="1.1" viewBox="0 0 7.3000002 7.9499998" width="7.3000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45F" /></g></svg> and <svg style="vertical-align:-0.1638pt;width:12.225px;" id="M5" height="7.9499998" version="1.1" viewBox="0 0 12.225 7.9499998" width="12.225" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D464" /></g></svg> vanish in the limit of slow operation; short circuit in which again <svg style="vertical-align:-0.1638pt;width:7.3000002px;" id="M6" height="7.9499998" version="1.1" viewBox="0 0 7.3000002 7.9499998" width="7.3000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45F" /></g></svg> and <svg style="vertical-align:-0.1638pt;width:12.225px;" id="M7" height="7.9499998" version="1.1" viewBox="0 0 12.225 7.9499998" width="12.225" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D464" /></g></svg> vanish but in the limit of fast operation; maximum <svg style="vertical-align:-0.1638pt;width:7.3000002px;" id="M8" height="7.9499998" version="1.1" viewBox="0 0 7.3000002 7.9499998" width="7.3000002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45F" /></g></svg>; maximum <svg style="vertical-align:-0.1638pt;width:12.225px;" id="M9" height="7.9499998" version="1.1" viewBox="0 0 12.225 7.9499998" width="12.225" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D464" /></g></svg>. The behavior of the considered systems is explained by means of the proposed model. The derived formulae could be used for a quick estimation of <svg style="vertical-align:-0.1638pt;width:12.225px;" id="M10" height="7.9499998" version="1.1" viewBox="0 0 12.225 7.9499998" width="12.225" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D464" /></g></svg> and the temperatures of the working fluid at the hot and cold sides.

Mahmoud Huleihil

Bjarne Andresen

Generalized Performance Characteristics of Refrigeration and Heat Pump Systems

Recent developments in liquid technology have created a new class of fluids called “nanofluids” which are two-phase mixtures of a non-metal-liquid matrix and addon particles usually less than 100 nm in size. It is reputed that such liquids have a great potential for application. Indeed, many tests have shown that their thermal conductivity can be increased by almost 20% compared to that of the base fluids for a relatively low particle loading (of 1 up to 5% in volume). It is confirmed by experimental data and simulation results. In this study, the author considers an effect of impurity clustering by liquid density fluctuations as a natural mechanism for stabilizing microstructure of the colloidal solution and estimates the effect of fractal structure of colloidal particles on thermal conductivity of water. The results of this study may be useful for motivating choosing the composition of heat-transfer suspension and developing technology for making the appropriate nanofluid.

Alexander L. Shimkevich

On Clustering Impurities by Liquid Density Fluctuations

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xlink:href="#x44" /></g><g transform="matrix(.012,-0,0,-.012,36.863,19.862)"><use xlink:href="#x35" /></g><g transform="matrix(.012,-0,0,-.012,42.574,19.862)"><use xlink:href="#x2F" /></g><g transform="matrix(.012,-0,0,-.012,47.476,19.862)"><use xlink:href="#x32" /></g><g transform="matrix(.017,-0,0,-.017,53.812,15.775)"><use xlink:href="#x28" /></g><g transform="matrix(.017,-0,0,-.017,59.694,15.775)"><use xlink:href="#x1D45B" /></g><g transform="matrix(.017,-0,0,-.017,72.936,15.775)"><use xlink:href="#x3D" /></g><g transform="matrix(.017,-0,0,-.017,87.64,15.775)"><use xlink:href="#x36" /></g><g transform="matrix(.017,-0,0,-.017,92.978,15.775)"><use xlink:href="#x2D" /></g><g transform="matrix(.017,-0,0,-.017,96.19,15.775)"><use xlink:href="#x35" /></g><g transform="matrix(.017,-0,0,-.017,104.35,15.775)"><use xlink:href="#x30" /></g><g transform="matrix(.017,-0,0,-.017,112.509,15.775)"><use xlink:href="#x29" /></g></svg> spectrum series for francium atom are calculated. The calculated results are in excellent agreement with the 74 known experimentally measured levels (the absolute difference is less than 0.03 cm<sup>-1</sup>) and 58 energy levels for highly excited states are predicted.

Huang Shizhong

Sun Qiufeng

Calculation of the Rydberg Energy Levels for Francium Atom

Image fields generated by a bunch of charged particles between two parallel perfectly conducting plates are studied in detail. We derive exact analytical expressions for external fields of a charged relativistic bunch with a circular cross-section. Summation of image fields by the direct method invented by Laslett allows the infinite series to be represented in terms of elementary trigonometric functions.

B. Levchenko

Electric and Magnetic Fields Generated by a Charged Bunch between Parallel Conducting Plates


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					</g>
				</g>
			</svg> is still open. In the present paper we show, using standard Monte Carlo calculations, that the situation corresponds to a phase of mixed ordered structures quantified by an &#x201c;algebraic&#x201d; order parameter defined as the sum of densities of the existing ordered clusters. The introduced grandeur also characterizes the transitions towards the known pure ordered phases for the other values of <svg style="vertical-align:-0.0pt" id="M3" height="9.2749996" version="1.1" viewBox="0 0 10.4875 9.2749996" width="10.4875" xmlns="http://www.w3.org/2000/svg">
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						<text transform="matrix(1,0,0,-1,-71.95,64.63)">
							<tspan style="font-size: 11.21px; " x="0" y="0">𝑅</tspan>
						</text>
					</g>
				</g>
			</svg> as mentioned by the agreement of our results with those of the literature. The computation of the Cowley short range order parameter against <svg style="vertical-align:-0.0pt" id="M4" height="9.2749996" version="1.1" viewBox="0 0 10.4875 9.2749996" width="10.4875" xmlns="http://www.w3.org/2000/svg">
				<g transform="matrix(1.25,0,0,-1.25,0,9.275)">
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						<text transform="matrix(1,0,0,-1,-71.95,64.63)">
							<tspan style="font-size: 11.21px; " x="0" y="0">𝑅</tspan>
						</text>
					</g>
				</g>
			</svg> suggests that the central point is bicritical and is a state to cross when passing between the two pure phases.

Yahia Boughaleb

Mohammed Nouredine

Mohamed Snina

Rachid Nassif

Mohamed Bennai

Bicritical Central Point of <svg style="vertical-align:-3.41936pt" height="15.4375" version="1.1" viewBox="0 0 64.0625 15.4375" width="64.0625" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x1D43D" d="M434 650l-5 -28q-60 -8 -75 -20.5t-25 -69.5l-71 -395q-20 -107 -57.5 -168t-106.5 -94q-40 -18 -61 -20l-10 32q77 23 113 108q21 50 41 160l68 377q10 57 -1.5 69.5t-76.5 20.5l6 28h261z" /></g><g transform="matrix(.012,-0,0,-.012,7.825,15.187)"><path id="x46" d="M493 503l-29 -4q-13 56 -28 80q-13 22 -35.5 29.5t-78.5 7.5h-76q-22 0 -27.5 -5t-5.5 -27v-238h103q66 0 82.5 12t25.5 62h29v-193h-29q-9 54 -25.5 67t-82.5 13h-103v-181q0 -64 15 -78.5t84 -19.5v-28h-272v28q61 5 74.5 19.5t13.5 78.5v399q0 64 -13 78t-72 19v28&#xA;h440q1 -40 10 -147z" /></g><g transform="matrix(.012,-0,0,-.012,14.119,15.187)"><path id="x4E" d="M719 650v-28q-43 -2 -62 -15t-22 -44q-6 -47 -6 -169v-403h-31l-426 524h-2v-251q0 -111 6 -169q4 -37 24 -50.5t72 -16.5v-28h-237v28q45 2 64.5 16t23.5 49q6 62 6 171v220q0 54 -3 68.5t-17 32.5q-16 19 -34.5 26.5t-54.5 10.5v28h147l418 -502h3v246q0 117 -7 166&#xA;q-4 34 -24.5 47t-73.5 15v28h236z" /></g><g transform="matrix(.017,-0,0,-.017,27.362,11.112)"><path id="x2212" d="M535 230h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,41.114,11.112)"><use xlink:href="#x1D43D"/></g><g transform="matrix(.012,-0,0,-.012,48.888,15.187)"><path id="x53" d="M409 504l-29 -5q-16 60 -44.5 96t-86.5 36q-54 0 -82.5 -32t-28.5 -77q0 -51 30.5 -82.5t96.5 -65.5l35.5 -18t33 -19.5t33.5 -23.5l27 -25.5t24.5 -32t13.5 -36.5t6 -45q0 -80 -62 -134.5t-160 -54.5q-47 0 -98 15q-22 7 -50 21q-8 23 -27 155l30 7q7 -27 18 -52&#xA;t30 -51.5t49 -42.5t67 -16q56 0 88 32.5t32 87.5q0 51 -31.5 82t-98.5 67q-80 44 -110 73q-55 53 -55 124q0 75 56 126.5t150 51.5q53 0 126 -23z" /></g><g transform="matrix(.012,-0,0,-.012,54.528,15.187)"><use xlink:href="#x4E"/></g></svg> Ising Model Phase Diagram

A photonic analogue of Klein tunneling (KT), that is, of the exotic property of relativistic electrons to
pass a large repulsive and sharp potential step, is proposed for pulse propagation in a nonuniform
fiber Bragg grating with an embedded chirped region. KT can be simply observed as the opening of
a transmission window inside the grating stop band, provided that the impressed chirp is realized
over a length of the order of the analogue of the Compton wavelength.

Stefano Longhi

Klein Tunneling of Light in Fiber Bragg Gratings

A comparative study between effects of Mn and Al on the properties of ZnO varistor sintered at 1200<svg style="vertical-align:-0.17554pt;width:15px;" id="M1" height="10.9125" version="1.1" viewBox="0 0 15 10.9125" width="15"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
		<g transform="translate(72,-63.27)">
			<text transform="matrix(1,0,0,-1,-71.95,68.5)">
				<tspan style="font-size: 8.75px; " x="0" y="0">∘</tspan>
			</text>

			<text transform="matrix(1,0,0,-1,-68.39,63.5)">
				<tspan style="font-size: 12.50px; " x="0" y="0">C</tspan>
			</text>

		</g>
	</g>
</svg> is investigated by XRD, SEM hardness, and I-V measurements. Although both Mn and Al do not influence the well-known peaks related to wurtzite structure of ZnO ceramics, some other unknown peaks could be formed at higher doping content (<svg style="vertical-align:-1.29163pt;width:42.525002px;" id="M2" height="12.3" version="1.1" viewBox="0 0 42.525002 12.3" width="42.525002"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,12.3)">
		<g transform="translate(72,-62.16)">
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				<tspan style="font-size: 12.50px; " x="0" y="0">≥</tspan>
				<tspan style="font-size: 12.50px; " x="12.027886" y="0">0</tspan>
				<tspan style="font-size: 12.50px; " x="18.279387" y="0">.</tspan>
				<tspan style="font-size: 12.50px; " x="21.405136" y="0">1</tspan>
				<tspan style="font-size: 12.50px; " x="27.656635" y="0">0</tspan>
			</text>

		</g>
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</svg>). Also, the shape and size of grains are clearly different for both dopants. Average crystalline diameters, deduced 
from XRD analysis, are between 42&#x2009;nm and 62&#x2009;nm, which are 50 times lower than those obtained from SEM micrographs, while the oxygen vacancies deduced from EDAX analysis, are gradually decreased by doping content for both dopants. 
Interestingly, the values of breakdown field, nonlinear coefficient and barrier height are found to be higher in Mn samples as compared to Al samples, while the opposite is reported for leakage currents, hardness, and electrical conductivities. The values of <svg style="vertical-align:-3.13504pt;width:19.9625px;" id="M3" height="14.2375" version="1.1" viewBox="0 0 19.9625 14.2375" width="19.9625"  xmlns="http://www.w3.org/2000/svg">
	<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
		<g transform="translate(72,-60.61)">
			<text transform="matrix(1,0,0,-1,-71.95,63.79)">
				<tspan style="font-size: 12.50px; " x="0" y="0">𝐸</tspan>
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			<text transform="matrix(1,0,0,-1,-63.02,60.66)">
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	</g>
</svg> 
are changed from 2.67&#x2009;V/cm to 41.67&#x2009;V/cm for Al, and from 1928&#x2009;V/cm to 6571&#x2009;V/cm for Mn. The conductivity of Al samples is higher than that of ZnO, and it is nearly (103&#x2013;105) times the conductivity of Mn samples. These 
results are discussed in terms of the difference of magnetic moment and valence state between these two additives.

A. Sedky

E.  El-Suheel

A Comparative Study between the Effects of Magnetic and Nonmagnetic Dopants on the Properties of ZnO Varistors

We study the dynamics of transverse oscillations of a suspended carbon nanotube into which electron current is injected from the tip of a scanning tunneling microscope (STM). In this case
the correlations between the displacement of the nanotube and its charge state, determined by the
position-dependent electron tunneling rate, can lead to a “shuttle-like” instability for the transverse
vibrational modes. We find that selective excitation of a specific mode can be achieved by an
accurate positioning of the STM tip. This result suggests a feasible way to control the dynamics of
this nano-electromechanical system (NEMS) based on the “shuttle instability.”

F. Santandrea

Selective Excitations of Transverse Vibrational Modes of a Carbon Nanotube through a “Shuttle-Like” Electromechanical Instability

We performed a two-variable canonical transformation on the time momentum operator, and without loss of generality we carried out a three-variable transformation on the coordinate and momentum space operators to trivialize the Hamiltonian operator of the system. Fortunately, this operation separates the time-coordinate and space coordinate naturally, and the wave function of the time-dependent Harmonic Oscillator is evaluated via the generator.

Akpan N. Ikot

Louis E. Akpabio

Ita O. Akpan

Michael I. Umo

Oladunjoye A. Awoga

Alice B. Nyong

On the Canonical Transformation of Time-Dependent Harmonic Oscillator

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