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The possibilities of LaF3–Er3+crystal to obtain cascade lasing with CW pumping at 0.52 μm wavelength are considered. The conditions for the formation of inverse populations between Stark levels of neighboring manifolds are determined. It is shown that, at 100 K and CW pump intensity , it is possible to obtain simultaneously laser radiation at 3.21 and 2.88 μm wavelengths. [ABSTRACT FROM AUTHOR]

Randomized machine learning focuses on problems with considerable uncertainty in data and models. Machine learning algorithms are formulated in terms of a functional entropy-linear programming problem. We adapt these algorithms to forecasting problems on an example of the evolution of thermokarst lakes area in permafrost zones. Thermokarst lakes generate methane, a greenhouse gas affecting climate change. We propose randomized machine learning procedures using dynamic regression models with random parameters and retrospective data (climatic parameters and remote sensing of the Earth's surface). The randomized machine learning algorithm developed below estimates the probability density functions of model parameters and measurement noises. Randomized forecasting is implemented as algorithms transforming the optimal distributions into the corresponding random sequences (sampling algorithms). The randomized forecasting procedures and technologies are trained, tested, and then applied to forecast the evolution of thermokarst lakes area in Western Siberia. [ABSTRACT FROM AUTHOR]

As the pig industry develops rapidly, various problems are increasing both inside and outside pig houses. In particular, in the case of pig houses, it is difficult to solve the main problems even if automation and mechanization are applied with Information and Communications Technologies (ICT). The air recirculation technology can be applied as a technology that can solve these typical problems in the pig industry, such as growth environment, livestock disease, odor emission, energy cost, and pig productivity. The air recirculated ventilation system (ARVS) can minimize the inflow of air from the outdoors and recycle the internal thermal energy of the pig house. The ARVS consists of (1) an air scrubber module, (2) an external air mixing module, (3) a UV cleaning module, (4) a solar heat module, and (5) an air distribution module. In this study, the growth environment of piglets was predicted using a numerical model when the ARVS was applied. Since the concept of air recirculation was used, numerous equations for predicting the internal environment should be iteratively calculated. Furthermore, it was necessary to determine the optimum condition of the modules by applying various boundary conditions. Therefore, the model was designed for numerical analysis based on the balance equations of environmental factors inside the piglet room. For each module, the module coefficient and equations were considered based on the previous studies. The analysis was conducted according to the system diagram of each module, and the growth environment inside the piglet room was evaluated according to the various environmental conditions. As a result of calculating the numerical model, the ventilation rate of 40 CMM or more was advantageous to properly maintaining the gas environment. In the summer season, it was necessary to additionally use the cooling device and dehumidifier. In the winter season, when using a heat exchanger and solar module, was more advantageous for maintaining air temperature inside the piglet room. [ABSTRACT FROM AUTHOR]

Combining the concept of randomization with entropic criteria allows solutions to be obtained in the conditions of maximum uncertainty, which is very effective in machine learning and data processing. The application of this approach in data-based entropy-randomized evaluation of functions, randomized hard and soft machine learning, object clustering, and data matrix dimension reduction is demonstrated. Some applications of classification problems, forecasting the electric load of a power system, and randomized clustering of biological objects are considered. [ABSTRACT FROM AUTHOR]

The classic M/M/$m$/$n$ queueing model is modified by allowing a given task to require up to $m$ servers to be performed. Moreover, the maximum time that a task can wait in the queue before being executed is a random variable having an exponential distribution. Both FIFO (First In, First Out) and priority disciplines are considered. The case when $m=2$ is treated: the state space needed to fully describe the system is given, its size is calculated and the balance equations are presented when $n=1,2$ and 3. The queueing process can be used to model cluster-type multiprocessor computing systems.

It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics, respectively. These schemes are based on an unusual feature, a formal redoubling of the degrees of freedom. Several arguments to motivate the redoubling are put forward in classical and quantum mechanics to demonstrate that such a formalism is natural. [Display omitted] • Action formalism for classical, quantum, closed and open dynamics. • Systematic approach to the quantum–classical transition. • A formal reduplication of the degrees of freedom. [ABSTRACT FROM AUTHOR]

The hydrodynamic Kelvin-Voigt model of production systems with a flow method of organizing production is considered. The main macro parameters of the state of the production line and the relationship between them are determined. The analysis of the main characteristics of models of elastic elements, which are used to analyze the occurrence of the dynamic stresses in a moving conveyor belt, is presented. A boundary value problem for elastic longitudinal vibrations in a conveyor belt with a moving material is formulated. It is assumed that the deformation of the conveyor belt element corresponds to the Kelvin-Voigt model and there is no sliding of the moving material on the belt. When determining the forces of resistance to motion acting on an element of the belt, the recommendations of DIN 22101: 2002-08 were used. The analysis of the Kelvin-Voigt model of the elastic element is carried out and the distinctive features of the model are demonstrated. The justification of the choice of the Kelvin-Voigt model of an elastic element for describing the process of occurrence of the longitudinal vibrations in a conveyor belt is given. The dependence of the non-uniform flow of material and the magnitude of tensions in the belt is estimated. An expression is written for the speed of propagation of disturbances along a moving conveyor belt with the material. The reasons for the acceleration and deceleration of the conveyor belt associated with the uneven supply of material at the entrance of the transport system are determined. The relationship between the speed of a conveyor belt and the mass of material along a section of the conveyor is demonstrated. It is shown that an increase in the power of the electric motor at the start and acceleration of the conveyor belt, as well as a decrease in power during the braking and stopping of the conveyor belt, is the cause of the appearance of dynamic stresses in it. The characteristic phases of the initial movement of the conveyor belt with the material are analyzed. The process of occurrence of dynamic tensions with the constant and variable acceleration of the conveyor belt for the phase of acceleration and deceleration of the conveyor belt is investigated. For the analysis, a dimensionless model of a conveyor line was used. An expression is obtained for static and dynamic tensions in the conveyor belt. The amplitude of oscillations of dynamic stresses and the characteristic time of damping of oscillations in a conveyor belt is estimated. A quadratic dependence of the speed of damping of a wave of dynamic tensions with an increase in the oscillation frequency is demonstrated. An inversely proportional dependence of the characteristic decay time of the generated dynamic tensions on the value of the viscosity coefficient of the composite material of the conveyor belt is shown.

A hydrodynamic model of production systems with a flow method of organizing production is considered. The basic macro-parameters of the state of the production flow line and the relationship between them are determined. The choice of a lot of moment approximation for modelling the production line is justified. It is shown that the conveyor-type flow line is a complex dynamic system with distributed parameters. The boundary value problem is formulated for the longitudinal vibrations of the conveyor belt when the material moves along the transportation route. It is assumed that there is no sliding of material along the conveyor belt, and the deformation that occurs in the conveyor belt is proportional to the applied force (Hooke's elastic deformation model). The significant effect of the uneven distribution of the material along the transportation route on the propagation velocity of dynamic stresses in the conveyor belt is shown. When constructing the boundary and initial conditions, the recommendations of DIN 22101: 2002-08 were used. The mechanism of the occurrence of longitudinal vibrations of the conveyor belt when the material moves along the transportation route is investigated. The main parameters of the model that cause dynamic stresses are determined. It is shown that dynamic stresses are formed as a result of a superposition of stresses in the direct and reflected waves. Analytical expressions are written that make it possible to calculate the magnitude of dynamic stresses in a conveyor belt and determine the conditions for the occurrence of destruction of the conveyor belt. The characteristic phases of the initial movement of the material along the technological route are considered. The process of the emergence of dynamic stresses with the constant and variable acceleration of the conveyor belt is investigated. The dynamics of stress distribution along the transportation route is presented. It is shown that the value of dynamic stresses can exceed the maximum permissible value, which leads to the destruction of the conveyor belt or structural elements. The transition period is estimated, which is required to ensure a trouble-free mode of transport operation during acceleration or braking of the conveyor belt. The use of dimensionless parameters allows us to formulate criteria for the similarity of conveyor systems.

The International Thermonuclear Experimental Reactor (ITER) tokamak can generate fusion energy in an acceptable method. In this study, the particle and energy equations were developed for T D , n 4 He , D D , n 3 He , D D , p T , and 3 He D , p 4 He fusion reactions and optimum conditions were determined to achieve the maximum gain using differing mixtures of fuel. Also, the particle and energy equations were solved using the zero-dimensional model, and the ITER90H-P plasma parameters were calculated by the numerical methods. The possibility regarding the presence of impurities was ignored in all our calculations. [ABSTRACT FROM AUTHOR]

As the pig industry develops rapidly, various problems are increasing both inside and outside pig houses. In particular, in the case of pig houses, it is difficult to solve the main problems even if automation and mechanization are applied with Information and Communications Technologies (ICT). The air recirculation technology can be applied as a technology that can solve these typical problems in the pig industry, such as growth environment, livestock disease, odor emission, energy cost, and pig productivity. The air recirculated ventilation system (ARVS) can minimize the inflow of air from the outdoors and recycle the internal thermal energy of the pig house. The ARVS consists of (1) an air scrubber module, (2) an external air mixing module, (3) a UV cleaning module, (4) a solar heat module, and (5) an air distribution module. In this study, the growth environment of piglets was predicted using a numerical model when the ARVS was applied. Since the concept of air recirculation was used, numerous equations for predicting the internal environment should be iteratively calculated. Furthermore, it was necessary to determine the optimum condition of the modules by applying various boundary conditions. Therefore, the model was designed for numerical analysis based on the balance equations of environmental factors inside the piglet room. For each module, the module coefficient and equations were considered based on the previous studies. The analysis was conducted according to the system diagram of each module, and the growth environment inside the piglet room was evaluated according to the various environmental conditions. As a result of calculating the numerical model, the ventilation rate of 40 CMM or more was advantageous to properly maintaining the gas environment. In the summer season, it was necessary to additionally use the cooling device and dehumidifier. In the winter season, when using a heat exchanger and solar module, was more advantageous for maintaining air temperature inside the piglet room.

In this paper, we consider the mechanism of a memory effect based on linear or nonlinear systems of balance equations. By considering a chain of balance equations, connecting each particle to the next by means of a memory kernel, it becomes possible to derive generalised expressions for the overall memory kernel that connects the initial particle to the last particle. We consider several different cases and types of systems, both linear and nonlinear. By assuming a general type of fractional integral operator to describe each balance equation, we derive an expression for the generalised memory which yields a more general type of fractional integral operator based on multivariate series. Some cases of this, such as multivariate Mittag-Leffler-type functions, are already known in mathematics, but they have never discovered real applications until now. [ABSTRACT FROM AUTHOR]

An algorithm of approximate solution of an essentially nonlinear problem of parameters of optically detected magnetic resonance in the ground state of alkali atoms in an optically dense medium under the conditions of strong narrow-band optical pumping that induces transparency of atomic medium and partial suppression of spin-exchange broadening is proposed. Straightforward solution of the Liouville's equation is complicated in this case by the fact that relaxation time of each of the levels of the hyperfine and Zeeman structures of the ground state is determined by populations of all other levels, which results in the necessity of solving a self-consistent problem in a multilevel system and requires using supercomputers, as a rule. In the present work, approximations that allow substantially simplifying and accelerating calculation are proposed. A two-beam MX-scheme of a magnetometric sensor is used as an example to compare the results of calculations with experimental data. [ABSTRACT FROM AUTHOR]

The classic M/M/m/n queueing model is modified by allowing a given task to require up to m servers to be performed. Moreover, the maximum time that a task can wait in the queue before being executed is a random variable having an exponential distribution. Both FIFO (First In, First Out) and priority disciplines are considered. The case when m = 2 is treated: the state space needed to fully describe the system is given, its size is calculated and the balance equations are presented when n = 1, 2 and 3. The queueing process can be used to model cluster-type multiprocessor computing systems. [ABSTRACT FROM AUTHOR]

External media surround almost all structures and bodies. Caused by thermodynamical reasons, the ambient medium, a fluid or a gas in this essay, is diffusing into or out of the solid. In consequence, the solid experiences changes in mass, volume and material properties. In order to formulate the thermodynamical balance equations for open systems of this type, it is taken into account that the diffusing liquid carries mass, linear and angular momentum, internal energy and entropy into or out of the solid. In this study, chemical reactions are omitted. All equations to be developed in this work are formulated in dependence on the spatial coordinates of the material points of the solid in the current configuration. In order to derive thermodynamically motivated models for the stress tensor, the specific entropy, the chemical potential and the fluid flux vector, an exemplary constitutive model for the Helmholtz free energy per unit mass is formulated and the second law of thermodynamics for open systems is evaluated by standard methods. Numerical simulations and analytical computations of a simple model problem display some fundamental properties of the theory. [ABSTRACT FROM AUTHOR]

Walter Noll (1925–2017) was an American mathematician of German birth who made lasting contributions to the foundations of continuum physics and the classical non-linear field theory. This essay is an attempt to put in a broader perspective Noll's methods and achievements in the hope that young generations of researchers may find their inspiration in the talent and depth of the old. By no means should this be considered as a historical account on the development of continuum mechanics through the second half of the twentieth century. We are content to illuminate Noll's precious legacy. [ABSTRACT FROM AUTHOR]

We present a micro-mechanical continuum model used for the description of dilatant granular materials with incompressible rotating grains for which the kinetic energy, in addition to the usual translational one, consists of other two terms owing to microstructural motions: in particular, it includes the dilatational expansions and contractions of the granules relative to one another, as well as the rotation movements of each grain compared to the others. Next, we propose a linear theory in which the representations of constitutive functionals are linear with respect to both the volume fraction and the micro-rotation gradients, and to the dissipative variables. At the end we test the linear model on a two-dimensional domain, in which the arising system of partial differential equations is solved using the finite element method; thus we obtain a numerical solution in the case of a simplified granular micromechanics. The obtained computations of the early granular dynamics are consistent with theoretical insights as deduced from the proposed model. Viscous and rotational contributions to the granular dynamics have been identified and compared each others. [ABSTRACT FROM AUTHOR]

The qualifier "ephemeral" was proposed for continuous models of bodies, such as gases, for which the generally tacit axiom of permanence of material elements fails to apply. Consequently, to their scrutiny, a Eulerian (local) approach is mandatory, such as one adopted, eg, in molecular dynamics. Within the scheme of ephemeral continua,we discuss here 3 essential subclasses of bodies: (1) those undergoing energy-preserving processes (in this sense hyperelastic), (2) hypoelastic bodies inspired by a type proposed by Truesdell, and (3) a number of minor ones. We re-examine the essential issues of the general format focusing on the proposal of appropriate concepts of strains and strainings. [ABSTRACT FROM AUTHOR]

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: The distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a departure epoch. The constraint for this result to be valid is that arrivals, and also service completions, with probability one occur individually, i.e., not in batches. We show that it is easy to write down somewhat similar balance equations for multidimensional queue-length processes for a quite general network of multiclass multiserver queues. We formally derive those balance equations under a general framework. They are called distributional relationships and are obtained for any external arrival process and state-dependent routing as long as certain stationarity conditions are satisfied and external arrivals and service completions do not simultaneously occur. We demonstrate the use of these balance equations, in combination with PASTA, by (1) providing very simple derivations of some known results for polling systems and (2) obtaining new results for some queueing systems with priorities. We also extend the distributional relationships for a nonstationary framework. [ABSTRACT FROM AUTHOR]

This study aims to develop constitutive equations for linear thermoelastic analysis of a composite material having piezoelectric feature and reinforced by arbitrary a fiber family. Fiber-reinforced composite media are assumed to be of anisotropic nature and are considered to be compressible due to their piezoelectric properties. Besides, it is assumed that the fiber family is inextensible. In addition, since the composite material is insensitive to the directional change along the fiber, it is mathematically unaffected by the change B→−B of fiber vector, so a symmetric a symmetric tensor, which is the outer product of the components of the fiber vector, is defined. The basis of this work is the equations of electro-thermomechanical equilibrium equations, fiber deformation geometry and kinematics. The use of constitutive axioms has shown that the stress potential is dependent on the Green deformation tensor, the fiber distribution tensor, the electric field vector and the absolute temperature, and the heat vector function is dependent on together with these magnitudes the gradient of the temperature field. Because of the anisotropic nature of the composite media, the stress potential and heat vector functions are found in approximate theories, and all of the interactions are considered as linear and series expansion is performed. Field equations are found as a result of substituting the expressions in equilibrium equations and the linear constitutive equations of symmetric stress, polarization and heat flux vector written in spatial coordinates. [ABSTRACT FROM AUTHOR]

We consider typical problems of the field called the finite time thermodynamics (also called the optimization thermodynamics). We also outline selected formal methods applied to solve these problems and discuss some results obtained. It is shown that by introducing constraints imposed on the intensity of fluxes and on the magnitude of coefficients in kinetic equations, it is possible not only to investigate limiting possibilities of thermodynamic systems within the considered class of irreversible processes, but also to state and solve problems whose formulation has no meaning in the class of reversible processes. This article is part of the themed issue ‘Horizons of cybernetical physics’. [ABSTRACT FROM AUTHOR]

A method to generate geometric pseudo-spectral spatial discretization schemes for hyperbolic or parabolic partial differential equations is presented. It applies to the spatial discretization of systems of conservation laws with boundary energy flows and/or distributed source terms. The symplecticity of the proposed spatial discretization schemes is defined with respect to the natural power pairing (form) used to define the port-Hamiltonian formulation for the considered systems of balance equations. The method is applied to the resistive diffusion model, a parabolic equation describing the plasma dynamics in tokamaks. A symplectic Galerkin scheme with Bessel conjugated bases is derived from the usual Galerkin method, using the proposed method. Besides the spectral and energetic properties expected from the symplecticity of the method, it is shown that more accurate approximation of eigenfunctions and reduced numerical oscillations result from this choice of conjugated approximation bases. Finally, the obtained numerical results are validated against experimental data from the tokamak Tore Supra facility. [ABSTRACT FROM AUTHOR]

The subject of this comprehensive study is the general (mathematical) modeling of sharp (i.e. two-dimensional) interfaces without and with their own thermodynamical activity. We provide essential tools for the modeling of body-interface systems. Important items of the kinematics of singular (moving) interfaces as well as balance equations at interfaces will be addressed. Problems connected with material representation will be discussed. Special interfacial balances for mass, impulse, angular momentum, energy, mass of a tracer and of entropy will be considered including the discussion of special cases. As an illustrative example, a continuous model for a body with loss of material (e.g. due to mechanical treatment) will be developed in the framework presented. [ABSTRACT FROM AUTHOR]

Neste estudo considera-se o problema de minimização de variações de geopotencial, na resolução de equações de balanço. Duas abordagens são discutidas: a primeira é a modificação de equações de inicialização para eliminar o problema de ausência de elípticidade e a segunda é a utilização de informação sobre distribuição de regiões não elípticas na solução de equações originais de balanço. Realiza-se uma análise de uma das versões de equações modificadas para modelos barotrópico e baroclínico da atmosfera. Por outro lado, um algoritmo de solução de equações de balanço com as pequenas variações de geopotencial é proposto, e sua eficiência é comparada com a do algoritmo convencional de inicialização.In this study, the problem of geopotential variations minimization in the solution of balance equations is considered. Two approaches are discussed: the first is a modification of initialization equations in order to avoid the problem of non-ellipticity, and the second is the use of information on the distribution of non-elliptic regions for solution of the original balance equations. An analysis of a version of the modified balance equations is made for the case of barotropic and baroclinc models of the atmosphere. On the other hand, a solution algorithm of the balance equations, which allows small variations of the geopotential field, is proposed and its efficiency is compared to that of the conventional initialization algorithm.

To eliminate the fast gravitational waves of great amplitude, which are not observed in the real atmosphere, the initial fields for numerical schemes of atmosphere forecasting and modeling systems are usually adjusted dynamically by applying balance relations. In this study we consider different forms of the balance equations and for each of them we detect the nonelliptic regions in the gridded atmosphere data of the Southern Hemisphere. The performed analysis reveals the geographical, vertical and zonally averaged distributions of nonelliptic regions with the most concentration in the tropical zone. The area of these regions is essentially smaller and less intensive for more complete and physically justified balance relations. The obtained results confirm the Kasaharas assumption that ellipticity conditions are violated in the actual atmospheric fields essentially due to approximations made under deriving the balance equations.Para eliminar as ondas gravitacionais rápidas de grande amplitude, as quais não se observam na atmosfera real, os campos iniciais para esquemas numéricos de sistemas de modelagem e previsão atmosférica são usualmente ajustados dinamicamente aplicando as relações de balanço. Neste estudo consideramos formas diferentes de equações de balanço e para cada uma dessas detectamos as regiões não elípticas nos dados atmosféricos do Hemisfério Sul. A analise realizada mostra a distribuição geográfica, vertical e média zonal de regiões não elípticas com maior concentração na zona tropical. A área dessas regiões é essencialmente reduzida e a intensidade é visivelmente menor para as relações de balanço mais completas e fisicamente justificáveis. Os resultados obtidos confirmam a suposição de Kasahara de que as condições de ellipticidade são violadas nos campos atmosféricos reais essensialmente devido às aproximações feitas em dedução das equações de balanço.

Extended Thermodynamics of dense gases with an arbitrary but fixed number of moments has been recently studied in literature. As usual in Extended Thermodynamics, in the field equations some unknown functions appear; restriction on their generalities is obtained by imposing the entropy principle, the Galilean relativity principle, and some symmetry conditions. The solution of these conditions has been obtained by using a Taylor expansion around equilibrium, without proving its convergence but only assuming it. In this article, we find an exact solution without Taylor’ s expansion so avoiding the problem of proving convergence. It will be found through a kinetic type approach. It is not a pure kinetic approach because we do not know the distribution function, but the techniques that are used are similar. If we expand this exact solution around equilibrium, we find the most significative part of the closure previously obtained with the macroscopic approach. [ABSTRACT FROM PUBLISHER]

This paper illustrates Gabrio Piola’s view on continuum models, especially how contact actions are defined. Piola presented his mechanical theory before the 1850s, in an attempt to generalize Lagrange’s analytical mechanics. He conceived, among the rest, an ideal state for physical bodies (which nowadays we would call a natural state), a very general set of what we would now call state variables, and obtained balance equations via the superposition of a rigid infinitesimal motion on the present configuration. These views look quite modern even today and seem to historically precede among other things the introduction of structured continua. [ABSTRACT FROM AUTHOR]

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[Display omitted] • We solved the full set of physical balance equations for mantle-crust evolution. • Computed timings of continental growth are similar to global detrital zircon ages. • Continental growth was an episodic rather than steady state process. This paper presents the computational basis for the study of Walzer and Hendel (2022), who consider the relationships between continental growth, sedimentary geology, natural climate change, and ice ages. Here we solve the full set of balance equations for mass, energy, momentum, and angular momentum for a 3D spherical-shell mantle. The assumed radial distribution of viscosity is given in Appendix B. Furthermore, the modeled viscosity depends on temperature and water concentration. The modeled mantle is internally heated by the radioactive decay of 238U, 235U, 232Th, and 40K. The heat-producing elements are redistributed by chemical differentiation in spatial regions due to partial melting. Thus, in a simplified way, continental material is formed, which accumulates at the surface of a sphere, moves sideways in a non-prescribed way due to flow, and accretes to form continents. The growth curve of the total mass of continental crust resembles that of realistic geological models. We present in Appendix B the Grüneisen parameter, adiabatic temperature, thermal expansivity, and specific heat as a function of depth. The temporal distribution of juvenile additions to the continents, as obtained using our model, has a marked resemblance to global detrital zircon ages published by Puetz and Condie (2019, 2022). The results indicate the continental crust grew in an episodic manner rather than by steady state. [ABSTRACT FROM AUTHOR]

The fluorescence polarization kinetics of fluorescent organic molecules and molecules with two interconverting photoisomeric forms and fixed molecular skeletons were investigated by numerical methods based on the solution of population balance equations. The depolarizing effect of the lowest triplet T state and the polarization time dependence for quasi-continuous-wave (cw) and pulsed photoexcitation were studied using model compounds. The fluorescence depolarization with cw excitation was characterized by times that were shorter than the T-state lifetime; for the isomers, also by times that correlated with the photoisomerization times. Intense pulsed photoexcitation distorted significantly the initial oscillator orientation distribution in the singlet S and S states and could lead to sign reversal of the polarization. [ABSTRACT FROM AUTHOR]

The design and analysis of the thermal/hydraulic systems in nuclear power plants necessitate system codes that can be used in the analysis of steady state and transient conditions. RELAP5 is one of the most commonly used system codes in nuclear organizations. RELAP5 is based on a two-fluid, non-equilibrium, non-homogeneous, hydrodynamic model for the transient simulation of the two-phase system behavior. This model includes six governing equations to describe the mass, energy, and momentum of the two fluids. The “non-conservative” numerical approximation form (which is the current version of RELAP5 code) is obtained through the manipulation of selected derivative terms in the equations including the linearization of the product terms in the time derivatives of the equations. In the non-conservative technique, the truncation errors introduced in the linearization process can produce mass and energy errors for some classes of transients during time advancements, either resulting in (a) automatic reduction of time steps used in the advancement of the equations and increased run times or (b) the growth of unacceptably large errors in the transient results. To eliminate these difficulties, an optional numerical approach has been introduced in RELAP/SCDAPSIM/MOD4.0. This approach uses a more consistent set of “conservative” numerical approximations to solve non-linearized mass and energy governing equations. The RELAP/SCDAPSIM/MOD4.0 code, being developed as part of the international Severe Core Damage Analysis Package (SCDAP) Development and Training Program (SDTP), is the first version of RELAP5 rewritten to FORTRAN 90/95/2000 standards. This paper provides an overview of the original RELAP5 numerical approximations and describes the new theoretical approach. The second article introduces the strategic solution of the more conservative approach and presents some examples of transient problems that have been addressed utilizing this new approach. [ABSTRACT FROM AUTHOR]

This contribution is the third part in a series devoted to the fundamental link between discrete particle systems and continuum descriptions. The basis for such a link is the postulation of the primary continuum fields such as density and kinetic energy in terms of atomistic quantities using space and probability averaging.In this part, solutions to the flux quantities (stress, couple stress, and heat flux), which arise in the balance laws of linear and angular momentum, and energy are discussed based on the Noll’s lemma. We show especially that the expression for the stress is not unique. Integrals of all the fluxes over space are derived. It is shown that the integral of both the microscopic Noll–Murdoch and Hardy couple stresses (more precisely their potential part) equates to zero. Space integrals of the Hardy and the Noll–Murdoch Cauchy stress are equal and symmetric even though the local Noll–Murdoch Cauchy stress is not symmetric. Integral expression for the linear momentum flux and the explicit heat flux are compared to the virial pressure and the Green–Kubo expression for the heat flux, respectively.It is proven that in the case when the Dirac delta distribution is used as kernel for spatial averaging, the Hardy and the Noll–Murdoch solution for all fluxes coincide.The heat fluxes resulting from both the so-called explicit and implicit approaches are obtained and compared for the localized case. We demonstrate that the spatial averaging of the localized heat flux obtained from the implicit approach does not equate to the expression obtained using a general averaging kernel. In contrast this happens to be true for the linear momentum flux, i.e. the Cauchy stress. [ABSTRACT FROM AUTHOR]

The paper is mainly devoted to the balance equations for anisotropic fluids such as, for instance, liquid crystals and cell populations in extracellular liquids. The body is modelled as a mixture of reacting micropolar constituents, the micropolar structure being associated with an orientational momentum in terms of a inertia tensor. Next thermodynamic restrictions are derived for constitutive equations involving the temperatures, the mass densities, their gradients and the stretching tensors of the constituents. The whole set of evolution equations is then established. While current models in the literature involve a (first-order or a second-order) evolution equation for the director, the present approach leads to an evolution equation for the intrinsic angular velocity as it happens for rigid bodies. The relation to the main models appeared in the literature is provided and the reason for the different form of evolution equations is outlined. [ABSTRACT FROM AUTHOR]

General principles of a procedure for matching energy balances of thermal power plants (TPPs), whose use enhances the accuracy of information-measuring systems (IMSs) during calculations of performance characteristics (PCs), are stated. To do this, there is the possibility for changing values of measured and calculated variables within intervals determined by measurement errors and regulations. An example of matching energy balances of the thermal power plants with a T-180 turbine is made. The proposed procedure allows one to reduce the divergence of balance equations by 3-4 times. It is shown also that the equipment operation mode affects the profit deficiency. Dependences for the divergence of energy balances on the deviation of input parameters and calculated data for the fuel economy before and after matching energy balances are represented. [ABSTRACT FROM AUTHOR]

Magnetoelastic behavior of a magnetic sensitive material has been analyzed theoretically in the present paper. The theory is formulated in the context of continuum electromagnetics. The solid medium is supposed to be made of elastic material with magnetic sensitivity and to be nonlinear, homogeneous, compressible, isothermal, has anisotropy. Magneto-elastic response of the material will show up as a stress and a magnetization field. From the formulation belonging to the constitutive equations, it has been observed that the stress and the magnetization have been derived from a scalar-valued thermodynamic potential defined in calculations. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on Green deformation tensor, magnetic field, and temperature distribution. The free energy function has been represented by a power series expansion and the type and number of terms taken into consideration in this series expansion has determined the non-linearity of the medium. Constitutive equations of symmetric stress, magnetization field and asymmetric stress have been obtained in both material and spatial coordinates. The quasi-linear constitutive equations which on material coordinates have been obtained by expressions (63)-(65). The quasi-linear constitutive equations have been given in expressions (70)-(72) on spatial coordinates. Finally, the quasi-linear constitutive equations of the symmetric stress and magnetization field are substituted in the relevant balance equations to obtain the field equations. The field equations containing the unknowns uk and ϕ coordinates have been obtained by expressions (75) and (76). Solution of these field equations under initial and boundary conditions forms the mathematical structure of specified a boundary value problem. [ABSTRACT FROM AUTHOR]

This paper is the second part of a series dedicated to reviewing the fundamental link between discrete and continuum formulations, which is established by space averaging followed by probability density averaging. On obtaining the continuum balance laws of mass and linear momentum in the part I, here the balance laws of angular momentum and energy are re-derived from a discrete (atomistic/molecular) description. Different approaches (explicit and implicit) for the consideration of the potential energy are reviewed. Thereby for the explicit approach ambiguous possibilities for the localization of the potential energy are briefly discussed. Thereby we conclude that the explicit approach is preferable from the practical application point of view, however it becomes cumbersome when applied to multi-body interactions systems, whereas the implicit approach has no ambiguity in the localization of the potential energy to each particle and is easily applicable to any multi-body potential. Possible solutions for continuum fluxes (couple stresses, heat flux) are postponed until part III of the series. [ABSTRACT FROM PUBLISHER]

The paper deals with a reacting fluid mixture. The balance equations are stated both in the Lagrangian and in the Eulerian description. The entropy principle is stated in terms of the entropy growths of the single constituents rather than by the classical entropy transport equation. Next the thermodynamic restrictions on the constitutive functions are derived by assuming that the partial pressures, entropies and internal energies are functions of the temperature and the pertinent mass density. As a consequence, the rate of reaction is shown to be proportional to the chemical affinity via a non-linear function of pressure, temperature, and mass fractions. The chemical affinity is then shown to be the derivative of the Gibbs free energy with respect to the reaction coordinate if the free energy density is in the standard form of a function of temperature and pressure while such is not the case if the model is adopted for a mixture of perfect gases. [ABSTRACT FROM AUTHOR]

The class of models of production systems with in-line production organization, introduced by the author (2003) and widely used nowadays for constructing effective control systems of production lines is discussed in the paper. Conceptual provisions of the statistical theory of production lines, operating in the transient and steady modes are considered. New types of models that allow to combine the self-consistent object-technology at the micro-level and flow at the macro-level descriptions of the production line are proposed. To build unsteady equations of state of the production line, analytical design methods of technological trajectories of objects of labor are developed. The design methods of technological trajectories are based on the laws of conservation of the number of transferred technology resources on the object of labor at a given space-time structure of the technological process. The developed design methods of technological trajectories were used to construct continuum models of production lines that operate in transient modes. To describe the stochastic process of the transfer of technology resources on the object of labor, the distribution function of objects by states is introduced. A kinetic model of transient processes, the equation of which for the first time contains terms that take into account the normative technological trajectories of objects of labor, and the mechanism of interaction of objects of labor among themselves and the process equipment is constructed. Using the kinetic equation, multi-moment balance equations of the continuum flow model of the production line are written. It is shown that the equations of the model of objecttechnology description are interrelated and coordinated with the balance equations of continuum flow models through the level of the kinetic description of the production process. [ABSTRACT FROM AUTHOR]