253 research outputs found
Analysis of Dislocation Mechanism for Melting of Elements: Pressure Dependence
In the framework of melting as a dislocation-mediated phase transition we
derive an equation for the pressure dependence of the melting temperatures of
the elements valid up to pressures of order their ambient bulk moduli. Melting
curves are calculated for Al, Mg, Ni, Pb, the iron group (Fe, Ru, Os), the
chromium group (Cr, Mo, W), the copper group (Cu, Ag, Au), noble gases (Ne, Ar,
Kr, Xe, Rn), and six actinides (Am, Cm, Np, Pa, Th, U). These calculated
melting curves are in good agreement with existing data. We also discuss the
apparent equivalence of our melting relation and the Lindemann criterion, and
the lack of the rigorous proof of their equivalence. We show that the would-be
mathematical equivalence of both formulas must manifest itself in a new
relation between the Gr\"{u}neisen constant, bulk and shear moduli, and the
pressure derivative of the shear modulus.Comment: 19 pages, LaTeX, 9 eps figure
Calculation of thermal parameters of SiGe microbolometers
The thermal parameters of a SiGe microbolometer were calculated using
numerical modeling. The calculated thermal conduction and thermal response time
are in good agreement with the values found experimentally and range between
2x10 and 7x10 W/K and 1.5 and 4.5 ms, respectively. High sensitivity
of microbolometer is achieved due to optimization of the thermal response time
and thermal conduction by fitting the geometry of supporting heat-removing legs
or by selection of a suitable material providing boundary thermal resistance
higher than 8x10 cmK/W at the SiGe interface.Comment: 11 pages, 6 figure
Численные методы решения задач Коши с контрастными структурами
Modern numerical methods allowing to solve contrast structure problems in the most efficient way are described. These methods include explicit-implicit Rosenbrock schemes with complex coefficients and fully implicit backward optimal Runge–Kutta schemes. As an integration argument, it is recommended to choose the length of the integral curve arc. This argument provides high reliability of the calculation and sufficiently decreases the complexity of computations for low-order systems. In order to increase the efficiency, we propose an automatic step selection algorithm based on curvature of the integral curve. This algorithm is as efficient as standard algorithms and has sufficiently larger reliability. We show that along with such an automatic step selection it is possible to calculate a posteriori asymptotically precise error estimation. Standard algorithms do not provide such estimations and their actual error quite often exceeds the user-defined tolerance by several orders. The applicability limitations of numerical methods are investigated. In solving superstiff problems, they sometimes do not provide satisfactory results. In such cases, it is recommended to imply approximate analytical methods. Consequently, numerical and analytical methods are complementary.Изложены современные численные методы, позволяющие наиболее эффективно рассчитывать задачи с контрастными структурами. К ним относятся явно-неявные схемы Розенброка с комплексными коэффициентами и чисто неявные оптимальные обратные схемы Рунге-Кутты. В качестве аргумента целесообразно выбирать длину дуги интегральной кривой. Этот аргумент обеспечивает высокую надежность расчета и существенно снижает трудоемкость для систем уравнений невысокого порядка. Для повышения экономичности предложен алгоритм автоматического выбора шага по кривизне интегральной кривой. Этот алгоритм не уступает стандартным алгоритмам по экономичности, но существенно превосходит их по надежности. Показано, что при этом можно одновременно вычислять апостериорную асимптотически точную оценку погрешности методом Ричардсона. Стандартные алгоритмы автоматического выбора шага не могут дать таких оценок, а фактическая погрешность у них нередко на много порядков превышает заданную пользователем. Исследованы границы применимости численных методов. При решении задач сверхвысокой жесткости они могут не дать удовлетворительного ответа; в этих случаях следует переходить к приближенным аналитическим методам. Таким образом, численные и асимптотические методы являются взаимно дополняющими
Spontaneous emission of an atom placed near a nanobelt of elliptical cross-section
Spontaneous emission of an atom (molecule) placed near a nanocylinder of
elliptical cross-section of an arbitrary composition is studied. The analytical
expressions have been obtained for the radiative and nonradiative channels of
spontaneous decay and investigated in details.Comment: 35 pages, 11 figure
Violation of hyperbolicity in a diffusive medium with local hyperbolic attractor
Departing from a system of two non-autonomous amplitude equations,
demonstrating hyperbolic chaotic dynamics, we construct a 1D medium as ensemble
of such local elements introducing spatial coupling via diffusion. When the
length of the medium is small, all spatial cells oscillate synchronously,
reproducing the local hyperbolic dynamics. This regime is characterized by a
single positive Lyapunov exponent. The hyperbolicity survives when the system
gets larger in length so that the second Lyapunov exponent passes zero, and the
oscillations become inhomogeneous in space. However, at a point where the third
Lyapunov exponent becomes positive, some bifurcation occurs that results in
violation of the hyperbolicity due to the emergence of one-dimensional
intersections of contracting and expanding tangent subspaces along trajectories
on the attractor. Further growth of the length results in two-dimensional
intersections of expanding and contracting subspaces that we classify as a
stronger type of the violation. Beyond of the point of the hyperbolicity loss,
the system demonstrates an extensive spatiotemporal chaos typical for extended
chaotic systems: when the length of the system increases the Kaplan-Yorke
dimension, the number of positive Lyapunov exponents, and the upper estimate
for Kolmogorov-Sinai entropy grow linearly, while the Lyapunov spectrum tends
to a limiting curve.Comment: 11 pages, 11 figures, results reproduced with higher precision, new
figures added, text revise
Description of heterogeneous plasma microfield and optical properties of plasma by the QUIP model
Optical properties of plasmas are determined by presence of fluctuating microscopic electric field. The present work provides thorough analysis of contemporary models and points out their shortcomings. To overcome the latter, we take the QUIP (QUasi-Independent Particles) model derived ab initio. We provide generalization of the model allowing to account for microfield heterogeneity up to octupole term. We investigate convergence of the multipole series and show that higher order terms can be neglected. The model does not require laborious computations because all formulae are rather simple and are given in explicit form. This fact is an advantage of the proposed model compared to other contemporary models. We perform verification of the model via comparison with experiments. We emphasize that the comparison should be made with respect to the number of observed lines because this number strongly depends on the selected model. We outline experiments suitable for such testing. These are the experiments on Ar+Kr radiating plasma heated by laser radiation. In these experiments, the entire Ar+16 spectral series is observed. The QUIP model correctly describes the number of observed lines of the series, so its adequateness is justified. © 2020 Elsevier Inc
Efficient Numerical Integration Methods for the Cauchy Problem for Stiff Systems of Ordinary Differential Equations
The notion of stiffness of a system of ordinary differential equations is refined. The main difficulties encountered when solving the Cauchy problem for stiff systems are indicated. The advantages of switching to a new argument, the integral curve arc length, are demonstrated. Various mesh step selection criteria are discussed, and the integral curve curvature criterion is recommended. The most reliable implicit and explicit schemes suitable for solving stiff problems are presented. A strategy permitting an asymptotically accurate computation of the error of a numerical solution simultaneously with the solution itself is described. An analysis of chemical kinetics of hydrogen combustion in oxygen with allowance for 9 components and 50 reactions between them is provided as an illustration. © 2019, Pleiades Publishing, Ltd
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