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The purpose of this study is the application of the following concepts to the time discrete form. Variational Calculus, potential and kinetic energies, velocity proportional Rayleigh dissipation function, the Lagrange and Hamilton formalisms, extended Hamiltonians and Poisson brackets are all defined and applied for time-continuous physical processes. Such processes are not always time-continuously observable; they are also sometimes time-discrete.

The classical approach is developed with the benefit of giving only a short table on charge and flux formulation, as they are similar to the classical case just like all other formulation types. Moreover, an electromechanical example is represented as well.

Lagrange and Hamilton formalisms together with the velocity proportional (Rayleigh) dissipation function can also be used in the discrete time case, and as a result, dissipative equations of generalized motion and dissipative canonical equations in the discrete time case are obtained. The discrete formalisms are optimal approaches especially to analyze a coupled physical system which cannot be observed continuously. In addition, the method makes it unnecessary to convert the quantities to the other. The numerical solutions of equations of dissipative generalized motion of an electromechanical (coupled) system in continuous and discrete time cases are presented.

The formalisms and the velocity proportional (Rayleigh) dissipation function aforementioned are used and applied to a coupled physical system in time-discrete case for the first time to the best of the author’s knowledge, and systems of difference equations are obtained depending on formulation type.

The purpose of this paper is to analyze the dynamical state of a discrete time engineering/physical dynamic system. The analysis is performed based on observability, controllability and stability first using difference equations of generalized motion obtained through discrete time equations of dissipative generalized motion derived from discrete Lagrange-dissipative model [{L,D}-model] for short of a discrete time observed dynamic system. As a next step, the same system has also been analyzed related to observability, controllability and stability concepts but this time using discrete dissipative canonical equations derived from a discrete Hamiltonian system together with discrete generalized velocity proportional Rayleigh dissipation function. The methods have been applied to a coupled (electromechanical) example in different formulation types.

An observability, controllability and stability analysis of a discrete time observed dynamic system using discrete equations of generalized motion obtained through discrete {L,D}-model and discrete dissipative canonical equations obtained through discrete Hamiltonian together with discrete generalized velocity proportional Rayleigh dissipation function.

The related analysis can be carried out easily depending on the values of classical elements.

Discrete equations of generalized motion and discrete dissipative canonical equations obtained by discrete Lagrangian and discrete Hamiltonian, respectively, together with velocity proportional discrete dissipative function are used to analyze a discrete time observed engineering system by means of observability, controllability and stability using state variable theory and in the method proposed, the physical quantities do not need to be converted one to another.

This paper aims to present an unconditionally energy-stable scheme for approximating the convective heat transfer equation.

The scheme stems from the generalized positive auxiliary variable (gPAV) idea and exploits a special treatment for the convection term. The original convection term is replaced by its linear approximation plus a correction term, which is under the control of an auxiliary variable. The scheme entails the computation of two temperature fields within each time step, and the linear algebraic system resulting from the discretization involves a coefficient matrix that is updated periodically. This auxiliary variable is given by a well-defined explicit formula that guarantees the positivity of its computed value.

Compared with the semi-implicit scheme and the gPAV-based scheme without the treatment on the convection term, the current scheme can provide an expanded accuracy range and achieve more accurate simulations at large (or fairly large) time step sizes. Extensive numerical experiments have been presented to demonstrate the accuracy and stability performance of the scheme developed herein.

This study shows the unconditional discrete energy stability property of the current scheme, irrespective of the time step sizes.

The purpose of this paper is to develop a time implicit discontinuous Galerkin method for the simulation of two‐dimensional time‐domain electromagnetic wave propagation on non‐uniform triangular meshes.

The proposed method combines an arbitrary high‐order discontinuous Galerkin method for the discretization in space designed on triangular meshes, with a second‐order Cranck‐Nicolson scheme for time integration. At each time step, a multifrontal sparse LU method is used for solving the linear system resulting from the discretization of the TE Maxwell equations.

Despite the computational overhead of the solution of a linear system at each time step, the resulting implicit discontinuous Galerkin time‐domain method allows for a noticeable reduction of the computing time as compared to its explicit counterpart based on a leap‐frog time integration scheme.

The proposed method is useful if the underlying mesh is non‐uniform or locally refined such as when dealing with complex geometric features or with heterogeneous propagation media.

The paper is a first step towards the development of an efficient discontinuous Galerkin method for the simulation of three‐dimensional time‐domain electromagnetic wave propagation on non‐uniform tetrahedral meshes. It yields first insights of the capabilities of implicit time stepping through a detailed numerical assessment of accuracy properties and computational performances.

In the field of high‐frequency computational electromagnetism, the use of implicit time stepping has so far been limited to Cartesian meshes in conjunction with the finite difference time‐domain (FDTD) method (e.g. the alternating direction implicit FDTD method). The paper is the first attempt to combine implicit time stepping with a discontinuous Galerkin discretization method designed on simplex meshes.

In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.

It is often observed in practice that the essential behavior of mathematical models involving many variables can be captured by a much smaller model involving only a few variables. Further, the simpler model very often displays oscillatory behavior of some sort, especially when critical problem parameters are varied in certain ranges. This paper attempts to supply arguments from the theory of dynamical systems for why oscillatory behavior is so frequently observed and to show how such behavior emerges as a natural consequence of focusing attention upon so‐called “essential” variables in the process of model simplification. The relationship of model simplification and oscillatory behavior is shown to be inextricably intertwined with the problems of bifurcation and catastrophe in that the oscillations emerge when critical system parameters, i.e. those retained in the simple model, pass through critical regions. The importance of the simplification, oscillation and bifurcation pattern is demonstrated here by consideration of several examples from the environmental, economic and urban areas.

The purpose of this paper is to show that there are some underlying principles of granular media that can be derived from statistical mechanics and that could be useful when considered in the context of computer simulations.

The fundamentals of statistical mechanics are presented and they are revised in order to set up a suitable approach for jammed static granular media. After a conceptual discussion about the entropy of granular matter, some specific statistical mechanics approaches that have been used for granular media are reviewed. Finally, a numerical simulation, conducted using an open source molecular dynamics code, is included as an illustrative example.

It is shown qualitatively how statistical mechanics can be used to analytically compute the expected statistical distribution of some quantities in numerical simulations.

The computation of entropy from histograms and the establishment of the constraints of the ensembles in simulations are still open issues.

Considering the entropy could set up new computational techniques. Initial arrangements could be analyzed in terms of their probability of occurrence and of their “distance” to the most probable state.

The paper includes the distribution of the mean force‐moment tensor component of a fast cyclic quasi isotropic compression process of a simple granular media. Results show how the system tends to an equilibrium state.

The purpose of this paper is to present an academic programme of pansystems research with a lot of new concepts, principles, methods. Universal consideration of philosophy‐mathematics‐technology is set forth with mega‐combination. The emphasis on the transfield internet‐like investigations is developed. Many theory‐methods of pansystems get further concise optimization.

The concrete contents of the paper include: historical megawave, philosophical stratagems, meta‐mathematics, meta‐methodology, technological realistic principles, unification and differentiation of encyclopedic branches, systems science, information theory, cybernetics, biosystems, generalized vitality, computer and IT, thinking science, logic, OR, AI, PR, DM, modernization of yinyang analysis combining dialectics, sociology, economics, meta‐relativity, generalized quantification and scale theory, general process of birth‐growth‐ageing‐disease‐death, the inheritance and development of 300 scholars' researches, etc.

All of the topics concerned with are reduced to the actualizations of PVOR – pansystems variational OR: V−d(xy)=^*0^*/PRR′P′/0^**, which is an integrated synthesis of 20‐PanStemCells of PanConcepts and PanMethod, and embodies a specific pansystems summarization for the core of the true and the good. Furthermore, the formula “Pansystems Researches=^*(PVOR/0^**/Pan54787721/Everything)+^*0^*=^*Pan–netlike connections of thoughts and methods” is expanded with concrete applications.

Provides information on pansystems research.

Proposes to posit a clear definition of the energy stored in general electromagnetic media.

A general setting of thermodynamics using differential geometry is used and it is shown how the Poynting identity fits in.

A general method of defining the energy storage and dissipation in a general media is stated.

It appears that the definition of the energy stored in a dispersive media is not a state variable and depends on the history of the field variation.

If an electromagnetic model has to be coupled to a mechanical or thermal one, the associated forces and/or heat dissipations may not be clearly defined if one merely knows the electromagnetic constitutive relations.

It proposes a very general setting for the thermodynamic of electrodynamic media.

Building on the Rayleigh‐Stevenson approach fictitious internal source distributions responsible for the leading near‐field contribution of the long wavelength scattering by a non‐dissipative dielectric prolate spheroid are derived. The equivalent multiline sources arising from every polarization of the incoming field on the segment between the foci can be regarded as the result of an ultimate contraction of the volume polarization in the spheroid, or plainly as prolonged multipoles. In the low‐frequency asymptotic solution of the first‐order in terms of ω the solutions involve line and strip currents, and biline and quadriline charges, the density distributions of which obey simple polynomial laws. Numerical examples are provided, demonstrating their significance in the calculation of near‐zone fields in comparison with the direct radiation of elementary sets of point sources approximating the multiline distributions. The range of validity of the low‐frequency expansion is estimated by comparing with results obtained using the T‐matrix method.