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Статті в журналах з теми "Generalized continuous media":
1
Zhuravlev, Viktor. "Exactly integrable models of the wave interaction with continuous spectrum." Izvestiya VUZ. Applied Nonlinear Dynamics 9, no. 2 (2001): 76–81. http://dx.doi.org/10.18500/0869-6632-2001-9-2-76-81.
Анотація:
Interaction with a continuous spectrum in inhomogeneous media is constructed the Laks representation of exactly integrable model of the wave by the generalized Lagrange identities method for the conjugated equations. The general analysis of the obtained equations and ways of their use in theoretical and applied physical problems of non-linear wave processes are carried out.
2
Gasilov, V. A., A. S. Boldarev, O. G. Olkhovskaya, D. S. Boykov, Yu S. Sharova, N. O. Savenko, and A. M. Kotelnikov. "MARPLE: software for multiphysics modelling in continuous media." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie) 24, no. 4 (September 29, 2023): 316–38. http://dx.doi.org/10.26089/nummet.v24r423.
Анотація:
The research code MARPLE was originally created to model high-speed dynamic processes caused by the action of high-intensity energy fluxes on matter. At present, it is a universal tool able to solve various continuum mechanics problems. The implemented physical models are the following: single-fluid two-temperature MHD model of plasma dynamics, including electron-ion energy exchange and generalized Ohm’s law; model of electrical and thermal conductivity taking into account the anisotropy in the magnetic field; radiative heat transfer: models pertinent to optically thin as well as optically thick media: techniques for taking into account radiative cooling losses, spectral multigroup diffusion transfer, laser radiation propagation etc.; model of multicomponent flow. The MARPLE code utilises modern computational technologies based on block structured and unstructured meshes. MARPLE works as MPI application for modern HPC systems. The paper presents examples of problems in plasma dynamics, magnetohydrodynamics, astrophysics, and solid thermomechanics solved by means of the MARPLE code. Исследовательский код MARPLE изначально создавался для моделирования высокоскоростных динамических процессов, вызванных воздействием на вещество интенсивных потоков энергии. В настоящее время это универсальный инструмент, способный решать различные задачи механики сплошных сред. Реализованы следующие физические модели: одножидкостная двухтемпературная МГД-модель динамики плазмы, включающая электрон-ионный обмен энергией и обобщенный закон Ома; модель электро- и теплопроводности с учетом анизотропии в магнитном поле; радиационный теплообмен: модели, относящиеся как к оптически тонким, так и к оптически толстым средам: методы учета радиационных потерь на охлаждение, спектральный многогрупповой диффузионный перенос, распространение лазерного излучения и т. д.; модель многокомпонентного течения. В коде MARPLE используются современные вычислительные технологии, основанные на блочно-структурированных и неструктурированных сетках. MARPLE работает как приложение MPI для современных высокопроизводительных вычислительных систем. В работе приведены примеры задач динамики плазмы, магнитогидродинамики, астрофизики и термомеханики твердого тела, решенных с помощью кода MARPLE.
3
Gasilov, Vladimir Anontol’evich, Aleksey Sergeevich Boldarev, Olga Gourgenovna Olkhovskaya, Dmitri Sergeevich Boykov, Yulia Sergeevna Sharova, Nikita Olegovych Savenko, and Alexey Mikhailovich Kotelnikov. "MARPLE: software for multiphysics modelling in continuous media problems." Keldysh Institute Preprints, no. 37 (2023): 1–40. http://dx.doi.org/10.20948/prepr-2023-37.
Анотація:
The research code MARPLE was originally created to model high-speed dynamic processes caused by the action of high-intensity energy fluxes on matter. At present, it is a universal tool able to solve various continuum mechanics problems. The implemented physical models are the following: single-fluid two-temperature MHD model of plasma dynamics, including electron-ion energy exchange and generalized Ohm's law; model of electrical and thermal conductivity taking into account the anisotropy in the magnetic field; radiative heat transfer: models pertinent to optically thin as well as optically thick media: techniques for taking into account radiative cooling losses, spectral multigroup diffusion transfer, laser radiation propagation etc.; model of multicomponent flow. Calculations are performed using wide-range equations of state, transport and optical data. The MARPLE code utilises modern computational technologies based on block structured and unstructured meshes consisting of tetrahedral, hexahedral, prismatic elements and their combinations. The solvers implement conservation laws using high-resolution techniques. We apply the physical splitting to solve the governing system. The object-oriented approach to software design is used, as well as methods of object and generic programming (C++ implementation language). Design of computational domains is provided by means of integrated SALOME open source CAD-CAE system. Marple works as MPI application for modern HPC systems. The paper presents examples of problems in plasma dynamics, magnetohydrodynamics, astrophysics, and solid thermomechanics solved by means of the MARPLE code.
4
Eisa Ali Alhazmi, Shareefa. "New Model for Solving Mixed Integral Equation of the First Kind with Generalized Potential Kernel." Journal of Mathematics Research 9, no. 5 (August 21, 2017): 18. http://dx.doi.org/10.5539/jmr.v9n5p18.
Анотація:
New technique model is used to solve the mixed integral equation (\textbf{MIE}) of the first kind, with a position kernel contains a generalized potential function multiplying by a continuous function and continuous kernel in time, in the space $L_{2} (\Omega )\times C[0,T],\, 0\leq T<1$, $\Omega$ is the domain of integration and $T$ is the time. The integral equation arises in the treatment of various semi-symmetric contact problems, in one, two, and three dimensions, with mixed boundary conditions in the mechanics of continuous media. The solution of the \textbf{MIE }when the kernel of position takes the potential function form, elliptic function form, Carleman function and logarithmic kernel are discussed and obtain in this work. Moreover, many special cases are derived.
5
Pai, David M. "Generalized f-k (frequency‐wavenumber) migration in arbitrarily varying media." GEOPHYSICS 53, no. 12 (December 1988): 1547–55. http://dx.doi.org/10.1190/1.1442436.
Анотація:
Migration requires one‐way wave continuation. In the spatial domain, one‐way wave equations are derived based on various approximations to an assumed dispersion relation. In the frequency‐wavenumber domain, the well known f-k method and the phase‐shift method are strictly valid only within homogeneous models and layered models, respectively. In this paper, a frequency‐wavenumber domain method is presented for one‐way wave continuation in arbitrarily varying media. In the method, the downward continuation is accomplished, not with plane waves individually as in the f-k or the phase‐shift method, but with the whole spectrum of plane waves simultaneously in order to account for the coupling among the plane waves due to lateral inhomogeneity. The method is based on a matrix integral equation. The method has the following merits: (1) The method is a generalization of the f-k and the phase‐shift methods, valid in arbitrarily varying models. (2) The method has physical interpretations in terms of upgoing and downgoing plane waves, and as such the method has well defined steps leading from full‐wave continuation (two‐way wave) to one‐way wave continuation for migration. (3) The method is rigorous; the only approximations in the method—other than the one‐way wave approximation necessary for migration—are the discretization of a continuous system (which is necessary in computer methods) and imperfections associated with the limited spatial aperture of the data; as such, the method can achieve high solution accuracy. (4) The method can be fast, since computations are mainly matrix‐vector multiplications, which are easily vectorizable. In particular, compared to spatial domain methods, I contend that the method is (1) more rigorous in one‐way wave theory, (2) more accurate in migration of high‐dip events, and (3) faster for smooth models. I applied the method to a few examples of zero‐offset data migration, including imaging a point diffractor below a dipping interface, migration with sharp lateral variations in velocity, and migration with smooth lateral variations in velocity.
6
Gutlyanskii, Vladimir, Olga Nesmelova, Vladimir Ryazanov, and Artyem Yefimushkin. "Logarithmic potential and generalized analytic functions." Ukrainian Mathematical Bulletin 18, no. 1 (March 9, 2021): 12–36. http://dx.doi.org/10.37069/1810-3200-2021-18-1-2.
Анотація:
The study of the Dirichlet problem in the unit disk $\mathbb D$ with arbitrary measurable data for harmonic functions is due to the famous dissertation of Luzin [31]. Later on, the known monograph of Vekua \cite{Ve} has been devoted to boundary-value problems (only with H\"older continuous data) for the generalized analytic functions, i.e., continuous complex valued functions $h(z)$ of the complex variable $z=x+iy$ with generalized first partial derivatives by Sobolev satisfying equations of the form $\partial_{\bar z}h\, +\, ah\, +\ b{\overline h}\, =\, c\, ,$ where it was assumed that the complex valued functions $a,b$ and $c$ belong to the class $L^{p}$ with some $p>2$ in smooth enough domains $D$ in $\mathbb C$. The present paper is a natural continuation of our previous articles on the Riemann, Hilbert, Dirichlet, Poincar\'{e} and, in particular, Neumann boundary-value problems for quasiconformal, analytic, harmonic, and the so-called $A-$harmonic functions with boundary data that are measurable with respect to logarithmic capacity. Here, we extend the corresponding results to the generalized analytic functions $h:D\to\mathbb C$ with the sources $g$ : $\partial_{\bar z}h\ =\ g\in L^p$, $p>2\,$, and to generalized harmonic functions $U$ with sources $G$ : $\triangle\, U=G\in L^p$, $p>2\,$. This paper contains various theorems on the existence of nonclassical solutions of the Riemann and Hilbert boundary-value problems with arbitrary measurable (with respect to logarithmic capacity) data for generalized analytic functions with sources. Our approach is based on the geometric (theoretic-functional) interpretation of boundary-values in comparison with the classical operator approach in PDE. On this basis, it is established the corresponding existence theorems for the Poincar\'{e} problem on directional derivatives and, in particular, for the Neumann problem to the Poisson equations $\triangle\, U=G$ with arbitrary boundary data that are measurable with respect to logarithmic capacity. These results can be also applied to semi-linear equations of mathematical physics in anisotropic and inhomogeneous media.
7
Das, Debraj, and Luca Giuggioli. "Dynamics of lattice random walk within regions composed of different media and interfaces." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 1 (January 1, 2023): 013201. http://dx.doi.org/10.1088/1742-5468/aca8f9.
Анотація:
Abstract We study the lattice random walk dynamics in a heterogeneous space of two media separated by an interface and having different diffusivity and bias. Depending on the position of the interface, there exist two exclusive ways to model the dynamics: (a) Type A dynamics whereby the interface is placed between two lattice points, and (b) Type B dynamics whereby the interface is placed on a lattice point. For both types, we obtain exact results for the one-dimensional generating function of the Green’s function or propagator for the composite system in unbounded domain as well as domains confined with reflecting, absorbing, and mixed boundaries. For the case with reflecting confinement in the absence of bias, the steady-state probability shows a step-like behavior for the Type A dynamics, while it is uniform for the Type B dynamics. We also derive explicit expressions for the first-passage probability and the mean first-passage time, and compare the hitting time dependence to a single target. Finally, considering the continuous-space continuous-time limit of the propagator, we obtain the boundary conditions at the interface. At the interface, while the flux is the same, the probability density is discontinuous for Type A and is continuous for Type B. For the latter we derive a generalized version of the so-called leather boundary condition in the appropriate limit.
8
Ladovskii, Igor V., Petr S. Martyshko, Alexander G. Tsidaev, and Denis D. Byzov. "A Method for Quantitative Interpretation of Stationary Thermal Fields for Layered Media." Geosciences 10, no. 5 (May 22, 2020): 199. http://dx.doi.org/10.3390/geosciences10050199.
Анотація:
A new method to solve thermal conjugacy problems is presented for layered models with a thermal conductivity jump at their boundaries. The purpose of this method is to approximate the inverse thermal conductivity coefficient, which has breaks, by using a combination of step functions. A generalized continuous operator is constructed in a continuous space of piecewise–homogeneous media. We obtained an analytical solution for the stationary problem of heat conjugacy in the layered model with finite thickness and with Dirichlet–Neumann conditions at the external boundaries. An algorithm was constructed for downward continuation of the heat flux to depths that correspond to the top of the mantle layer. The advantages of this method are illustrated by testing the crustal seismic, gravity and geothermal data of a study area in the Urals and neighboring regions of Russia. We examined statistical relations between density and thermal parameters and determined heat flux components for the crust and the mantle. The method enables a downward continuation of the heat flux to the base of the upper mantle and allows us to determine the thermal effects of the lateral and vertical features of deep tectonic structures.
9
Misra, Anil, Luca Placidi, and Daria Scerrato. "A review of presentations and discussions of the workshop Computational mechanics of generalized continua and applications to materials with microstructure that was held in Catania 29–31 October 2015." Mathematics and Mechanics of Solids 22, no. 9 (August 29, 2016): 1891–904. http://dx.doi.org/10.1177/1081286516649654.
Анотація:
A report on the workshop Computational mechanics of generalized continua and applications to materials with microstructure (Catania 29–31 October 2015) is provided. The constructive atmosphere that was present at the workshop in 2012 and the Euromech Colloquium in 2014, both in Cisterna di Latina, was repeated for this workshop in Catania. The objective of this meeting was to bring together experts within the CNRS International Associate Laboratory (LIA) Francois Cosserat–Tullio Levi Civita Coss & Vita in order to discuss topics of common interest. Particularly, the workshop was dedicated to the following projects of LIA: (i) computational mechanics of generalized continua; and (ii) nonlinearity and stability in continuous media. Also subjects related to the application of generalized continua to multiscale and smart materials were discussed. Approximately 25 Coss & Vita LIA members and other experts (mostly from France and Italy) gathered together, including PhD students and those students from the Scuola Superiore di Catania.
10
Othman, M. I., and Y. Q. Song. "Reflection and refraction of thermo-viscoelastic waves at the interface between two micropolar viscoelastic media without energy dissipation." Canadian Journal of Physics 85, no. 7 (July 1, 2007): 797–812. http://dx.doi.org/10.1139/p07-072.
Анотація:
Reflection and refraction of a plane harmonic wave at the interface between two viscoelastic media are studied under generalized thermo-viscoelastic theory. Using potential function, the governing equations reduce to two fourth-order ifferential equations. Coefficient ratios of reflection and refraction of different waves with the angle of incidence are obtained using continuous boundary conditions. By numerical calculations, the variation of coefficient ratios of reflection and refraction with the angle of incidence are illustrated graphically for aluminium–epoxy and magnesium crystal micropolar viscoelastic materials. Also, the effects of viscous and micropolar elastic are illustrated by numerical results in the theory of thermo-viscoelasticity without energy dissipation. PACS No.: 62.20.Dc
Дисертації з теми "Generalized continuous media":
1
Wazne, Abdallah. "Non-linear mechanical behavior of strongly heterogeneous media by the mechanics of generalized continuous media and homogenization methods." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0153.
Анотація:
L'objectif de cette thèse est d'étudier de manière exhaustive le comportement non linéaire des matériaux en treillis périodiques constitués de poutres de Timoshenko, en tenant compte des énergies de cisaillement, d'extension et de flexion, ainsi que de leurs interactions. Pour atteindre cet objectif, nous avons développé un ensemble complet de fonctions de forme non linéaires et dérivé les équations dynamiques non linéaires pour divers réseaux architecturés. Nous nous sommes concentrés sur l'intégration de la matrice de rigidité non linéaire et sur l'étude de l'impact de l'énergie non linéaire totale (y compris les modes de cisaillement, d'extension et de flexion) sur la réponse dynamique des matériaux architecturés. En outre, nous avons effectué une analyse comparative de la propagation des ondes dans différents matériaux architecturés, en tenant compte de l'influence de l'énergie non linéaire et de la contribution de chaque mode (extension, flexion et cisaillement) aux relations de dispersion. En outre, nous avons effectué des calculs d'homogénéisation dynamique discrète pour différents matériaux architecturés non linéaires et réalisé des analyses de propagation des ondes en tenant compte de l'effet des termes de second gradient à la fois en 1D et en 2DThe objective of this thesis is to comprehensively investigate the nonlinear behavior of periodic lattice materials made of Timoshenko beams, by considering shear, extension, and bending energies, as well as their interactions. To achieve this objective, we have developed a complete set of nonlinear shape functions and derived the nonlinear dynamical equations for various architected networks. Our focus has been on incorporating the nonlinear stiffness matrix and studying the impact of the full nonlinear energy (including shear, extension, and bending modes) on the dynamical response of architected materials. Furthermore, we have conducted a comparative analysis of wave propagation in different architected materials, considering the influence of nonlinear energy and the contribution of each mode (extension, flexion, and shear) to the dispersion relations. Additionally, we have performed discrete dynamical homogenization computations for different nonlinear architected materials and carried out wave propagation analyses taking into consideration the effect of second gradient terms in both 1D and 2D
2
Alavi, Seyed Ehsan. "Homogénéisation de milieux architecturés périodiques et quasi-périodiques vers des milieux continus généralisés." Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0305.
Анотація:
Cette thèse vise à revisiter les schémas d'homogénéisation d'ordre supérieur vers des continuums d'ordre ou de gradient supérieurs, successivement pour les matériaux et composites architecturés périodiques et quasi-périodiques, en se basant sur des principes variationnels et une extension de la condition de macrohomogénéité de Hill. Les méthodes d'homogénéisation continue sont exposées dans la première partie pour les milieux micropolaires et micromorphes, suivies par une présentation de l’homogénéisation discrète, alternative de l’homogénéisation continue.Nous avons étendu ces développements théoriques à la situation des matériaux quasi-périodiques, de microstructure régulière, qui peut être transformée en une configuration périodique de référence. L'idée commune aux méthodes d'homogénéisation périodique proposées (de nature continue ou discrète) est de décomposer le déplacement microscopique en une partie homogène représentative de la cinématique du milieu continu effectif adopté, et une fluctuation évaluée à partir d'un principe variationnel. En substance, les développements théoriques permettent l'élaboration de continuums enrichis (milieux continus généralisés) de type micromorphe, et des variantes qui en découlent en utilisant des conditions de dégénérescence appropriées. Des applications numériques ont été réalisées pour des matériaux architecturés et des composites à renforts de type inclusion sujets à de tels effets d'ordre supérieur en raison de leur architecture interne. Sur le plan théorique, les développements réalisés remédient à de nombreuses limitations des schémas d'homogénéisation d'ordre supérieur existants.Dans la partie II, les propriétés mécaniques effectives classiques et d'ordre supérieur des matériaux architecturés ont été évaluées sur la base de schémas d'homogénéisation discrets. En suivant l'idée d'une approche phénoménologique, des modèles consistants de type couple de contraintes de réseaux de poutres répétitifs ont été élaborés. Des milieux de Cosserat enrichis ont été élaborés dans l'esprit de la micromécanique, en adoptant des modèles de poutre de Timoshenko à un niveau microscopique, et en appliquant une méthode de continualisation vers un milieu de substitution effectif de Cosserat. La méthode de continualisation proposée s'avère précise et efficace en termes de calcul par rapport aux schémas d'homogénéisation continus et aux simulations par éléments finis réalisés sur la microstructure initiale. Un résultat essentiel des analyses effectuées est la quantification des effets de bord.Le contexte théorique qui sous-tend l'homogénéisation asymptotique quasi-périodique dans le cadre de l'élasticité anisotrope linéarisée est abordé dans la troisième partie. Différentes méthodologies d'évaluation des propriétés effectives quasi-périodiques ont été élaborées, conduisant à l'émergence de milieux effectifs à gradient de déformation. Les transformations conformes définissent une classe spécifique de transformations géométriques permettant de concevoir des matériaux architecturés générant un gradient de porosité interne, ce qui en fait de bons candidats pour des biosubstituts en biomécanique osseuseThis thesis aims to revisit higher-order homogenization schemes towards higher-order or higher gradient continua, successively for periodic and quasi-periodic architected materials and composites, based on variational principles and an extension of Hill macrohomogeneity condition. Continuous homogenization methods are exposed in Part I for micropolar and micromorphic media, followed by an exposition of the alternative discrete homogenization method.We have extended these theoretical developments to the situation of quasi-periodic materials, which still have a regular microstructure. The common idea to the proposed periodic homogenization methods of continuous or discrete nature is to split the microscopic displacement into a homogeneous part representative of the kinematics of the adopted effective continuum and a fluctuation evaluated from a variational principle. In substance, the theoretical developments allow the elaboration of enriched continua (generalized continua) of micromorphic type and all sub continua obtained using suitable degeneration conditions. Numerical applications have been made for architected materials and inclusion-based composites prone to higher-order effects due to their inner architecture. On the theoretical framework, the performed developments remedy many existing limitations of existing higher-order homogenization schemes.In Part II, repetitive lattice materials' effective classical and higher-order mechanical properties have been evaluated based on discrete homogenization schemes. Following the idea of a phenomenological approach, consistent couple stress models of repetitive beam lattices have been elaborated. Enriched Cosserat media have been derived in the spirit of micromechanics, adopting Timoshenko beam models at a microlevel, and applying a continualization method towards a Cosserat effective substitution medium. The proposed continualization method proves to be accurate and computationally efficient compared to continuous homogenization schemes and fully resolved finite element simulations. One key outcome of the performed analyses is the quantification of edge effects in the response of lattice structures, relying on the surface formulation of the extended Hill macrohomogeneity condition.The theoretical background underlying quasi-periodic asymptotic homogenization in the framework of linearized anisotropic elasticity deserves the development of Part III. Different methodologies for evaluating the effective quasi-periodic properties have been elaborated, leading to the emergence of strain gradient effective media. Conformal transformations define a specific class of geometrical mappings, allowing for designing compatible architected materials with inner porosity gradient, making them suitable bone biomechanics candidates
Частини книг з теми "Generalized continuous media":
1
Del Piero, Gianpietro. "Virtual Power and Pseudobalance Equations for Generalized Continua." In Continuous Media with Microstructure 2, 11–21. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28241-1_2.
2
Dubovik, V. M., B. Saha, and M. A. Martsenuyk. "Generalized Equations of Electrodynamics of Continuous Media." In The Present Status of the Quantum Theory of Light, 141–50. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5682-0_14.
3
Lau, W. H. O., M. Kumar, and S. Venkatesh. "A Generalised Cost-Aware Caching Scheme for Caching Continuous Media Objects in Best-Effort Network Environments." In Lecture Notes in Computer Science, 12–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-36385-8_2.
4
Steane, Andrew M. "Physics in curved spacetime." In Relativity Made Relatively Easy Volume 2, 178–88. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.003.0014.
Анотація:
Electromagnetic field theory, and the physics of continuous media (fluids, solids) in curved spacetime are discussed. Generalized Maxwell’s equations are written down and their justifaction is briefly presented. Then we turn to thermodynamics and continuous media. The concept of energy and momentum conservation is carefully expounded, and then the equations for fluid flow (continuity equation and Euler equation) are developed from the divergence of the energy tensor. The Bernoulli equation and the equation for hydrostatic equilibrium are obtained. The chapter then goes on to a general discussion of how general relativity operates and how gravitational phenomena are calculated and observed. The relation between gravity and other aspects of physics such as particle physics is discussed, along with the notion of general covariance.
5
Furbish, David Jon. "Fluids and Porous Media as Continua." In Fluid Physics in Geology. Oxford University Press, 1997. http://dx.doi.org/10.1093/oso/9780195077018.003.0006.
Анотація:
Let us anticipate that we wish to treat fluids as continuous substances at a microscopic scale. To see the motivation for this, it is instructive to consider the possibility of describing fluid behavior at a molecular scale by making use of Lagrangian mechanics to track the behavior of each molecule, just as we would describe the ballistics of a moving, rigid body. Consider describing the state of a simple diatomic molecule at some instant; to do this, we must decide what minimum set of coordinates completely specifies the position and configuration of the molecule. For example, we must specify its position within an inertial reference frame, which requires the three Cartesian coordinates x, y, and z. We also must specify its velocity with respect to this coordinate system, which requires the three corresponding components of velocity um, vm, and wm. The molecule may be spinning; to describe this, we must assign to the molecule three local coordinate axes to specify three angular coordinates that give its orientation within the inertial reference frame. Because the axis of rotation may not coincide with one of the local axes, we also must specify two angular coordinates that give the orientation of the axis of rotation within the local coordinate system. Finally, we must specify the angular velocity about this axis of rotation. Thus, in addition to specifying the mass of a molecule, we need twelve variables or generalized coordinates to specify its state. Moreover, we must know initial values of these twelve coordinates, just as we need to know the initial position and velocity of a ballistic body to track its course. To track the behavior of N molecules, we therefore must know N masses plus 12N initial position, velocity, and orientation coordinates. It becomes clear that to adopt this approach to describe the behavior of a fluid constitutes a formidable task! One has no choice but to abandon a molecular scale treatment and adopt a view involving the microscopic scale, where behaviors of individual molecules are ignored, and instead, the collective behavior of a suitably defined ensemble of molecules is treated in a statistical (average) sense in terms of bulk properties such as fluid density, temperature, and viscosity.
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"Mechanics of Generalized Media." In Applications of Tensor Analysis in Continuum Mechanics, 243–317. WORLD SCIENTIFIC, 2018. http://dx.doi.org/10.1142/9789813238978_0006.
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Ganghoffer, Jean-Francois, Hilal Reda, and Kamel Berkache. "Generalised continuum mechanics of random fibrous media." In Mechanics of Fibrous Networks, 49–73. Elsevier, 2022. http://dx.doi.org/10.1016/b978-0-12-822207-2.00003-9.
Тези доповідей конференцій з теми "Generalized continuous media":
1
Geskin, E. S. "Thermodynamics of Continuous Systems." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42676.
Анотація:
The formalism of the classical thermodynamics, for example Gibbs equations, is routinely and successfully applied to the highly non-equilibrium processes in dynamic systems. Such applications are based on the local equilibrium hypothesis. The presented paper discusses the conditions of the application of this hypothesis. It is shown that the local equilibrium hypothesis is applicable with no limitations to continuous systems. This application is validated by the solution of the Boltzmann equation. This solution was obtained by Enskog, Chapman and Bogolubov. From the Boltzmann equation follows that regardless of the initial state of the system the duration of its approach to the local equilibrium conditions by far less than the time scale of the evolution of the macro properties of the continuous media. This result shows that the local equilibrium is the intrinsic property of this media. Thus it is possible to apply the formalism of the non-equilibrium thermodynamics (the generalized variables, forces and fluxes) to description of the continuous system with no limitations. The derivation of the Carnot theorem is presented to show the effectiveness of such an application.
2
Hassell, Bryan, and Alfonso Ortega. "An Investigation of Scale Variation in Multi-Layer Mini- and Micro-Channel Heat Sinks in Single Phase Flow Using a Two Equation Porous Media Model." In ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. ASMEDC, 2009. http://dx.doi.org/10.1115/ht2009-88423.
Анотація:
Research in liquid cooled mini- and micro-channel heat sinks is growing due to the potentially high heat fluxes that can be dissipated with such devices. Ostensibly, mini- or microchannel heat sinks are derivatives of more generalized porous structures. They are porous, but the pores are continuous and deterministic in structure, with well defined geometries created by etching or cutting channels into solid base material. As such, deterministic small scale heat sinks of this type lend themselves to modeling using the well-developed theories for saturated porous media. Based on the principle that physical problems contain multiple scales with multiple objectives, it is of interest to examine the possibility that allowing scale change away from the heated surface in a multi-layered heat sink would yield greater global benefits. Modeled as a saturated porous medium, scale variation in stacked multi-layer microchannel heat sinks has been explored using an experimentally verified two equation porous model. This paper compares and rates scaling parameters based on the pressure drop across the heat sink along with the unit thermal resistance.
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Podhiny, John J., and Alfonso Ortega. "Analysis of Single-Phase Multi-Layer Heat Sinks Using a Porous Media Approach: Influence of Spatially Varying Porosity." In ASME 2013 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/ipack2013-73189.
Анотація:
Prior analyses and experiments have demonstrated that varying or scaling the number of fluid channels in each layer of a stacked multi-layer heat sink yields distinct advantages over traditional single-layer designs which use channels with high aspect ratios. Specifically, a design which implements scaling in order to vary the porosity (or equivalently, the number of channels) from one layer to the next allows a given thermal performance to be realized at a lower pressure drop than the corresponding non-scaled design. While previous studies use porous media theory for their analytical foundation just as the current studies do, they also focused on heat exchangers with machined channels, and have consequently been limited to discrete variation of the porosity (or number of channels) in each layer. Extending this approach by allowing for continuous porosity variation provides a generalized and powerful design method for scaled multi-layer heat exchangers by mathematically modeling them using two-equation volume averaged quantities. This approach also yields insight into the fundamental design parameters which control the performance of this class of heat exchangers, and suggests that their performance-governing parameters are similar to those which govern fin performance. This paper focuses primarily on the thermal behavior of these liquid cooled heat sinks which employ various scaling functions to define the spatial variation of porosity. Comparisons are made with available closed-form solutions as well as results available from prior studies of discretely-scaled designs. The results indicate that scaling laws which have not been investigated previously can likely yield further performance improvements relative to prior designs.
4
Xu, Pinghua, Wenbin Hu, Jia Wu, and Weiwei Liu. "Opinion Maximization in Social Trust Networks." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/174.
Анотація:
Social media sites are now becoming very important platforms for product promotion or marketing campaigns. Therefore, there is broad interest in determining ways to guide a site to react more positively to a product with a limited budget. However, the practical significance of the existing studies on this subject is limited for two reasons. First, most studies have investigated the issue in oversimplified networks in which several important network characteristics are ignored. Second, the opinions of individuals are modeled as bipartite states (e.g., support or not) in numerous studies, however, this setting is too strict for many real scenarios. In this study, we focus on social trust networks (STNs), which have the significant characteristics ignored in the previous studies. We generalized a famed continuous-valued opinion dynamics model for STNs, which is more consistent with real scenarios. We subsequently formalized two novel problems for solving the issue in STNs. In addition, we developed two matrix-based methods for these two problems and experiments on realworld datasets to demonstrate the practical utility of our methods.
5
Gazzo, S. "Anisotropic behaviours and strain concentration in lattice material evaluated by means of discrete homogenization." In AIMETA 2022. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902431-84.
Анотація:
Abstract. Lattice fibre materials are challenging the standard modelling approaches due to their specific nature that results in peculiar effective behaviours such as extremely anisotropic materials or generalized continuum media. In this context, the aim of this paper is to the determine qualitatively and quantitatively the role of the morphological and mechanical parameters by investigating simple archetypical microstructures. The study is conducted through an up-scaling approach making use of the Homogenization method of discrete periodic media in the framework of a variational approach. The results of the homogenization have been validated comparing the response of the continuum with the response of discrete models.
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Soltani, Ali, and Hassan Sayyaadi. "Deployment of Multi-Agent Robotic Systems in Presence of Obstacles." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24026.
Анотація:
The deployment of multi-agent systems in presence of obstacle deals with autonomous motion of agents toward a specified target by sensing each other and boundaries of obstacles. In this paper, asynchronous, scalable, distributed algorithm is used to deploy agents. Boundaries of obstacles are modeled by virtual agents. Algorithm was implemented by solving continuous n-median problem called generalized Fermat-Weber problem. It is shown that deployment is performed when position of real agents are the geometric median of their Voronoi cells. Simulation results show the validity of the proposed algorithm very well.
7
Li, Zhuoran, and Guan Qin. "Pore–Scale Study of Effects of Hydrate Morphologies on Dissociation Evolutions Using Lattice–Boltzmann Method." In Offshore Technology Conference. OTC, 2021. http://dx.doi.org/10.4043/31067-ms.
Анотація:
Abstract The natural gas hydrate, plentifully distributed in ocean floor sediments and permafrost regions, is considered a promising unconventional energy resource. The investigation of hydrate dissociation mechanisms in porous media is essential to optimize current production methods. To provide a microscopic insight in the hydrate dissociation process, we developed a Lattice Boltzmann (LB) model to investigate this multi–physicochemical process, including mass transfer, conjugate heat transfer, and gas transport. The methane hydrate dissociation is regarded as the reactive transport process coupled with heat transfer. The methane transport in porous media is modelled by the generalized LB method with the Bhatnagar-Gross-Krook (BGK) collision model. The mass transfer from hydrate to fluid phase is described by the hydrate kinetic and thermodynamic models. Finally, the conjugate heat transfer LB-model for heterogeneous media is added for solving the energy equation. In the numerical experiments, we primarily investigated the effects of different hydrate distribution morphologies such as pore–filling, grain–coating, and dispersed on the hydrate dissociation process. From simulations, we found that in general, the dissociation rate and the methane average density rapidly approached the maximum value and then decreased with fluctuation during the dissociation process. This trend is due to that the endothermic reaction heat decreased the temperature, resulting in decelerating the dissociation. The average temperature decreased to minimum value instantaneously as hydrate started to dissociate. After the minimum value, the average temperature would increase slowly, accompanied by the thermal stimulation and hydrate consumption, displaying a valley shape of the temperature curve. We also found that the whole dissociation process and permeability–saturation relations are significantly affected by the hydrate morphologies. Under the same hydrate saturation, the dispersed case dissolves the fastest, whereas the grain–coating case is the slowest. Furthermore, we proposed a general permeability–saturation relation applicable for three cases, filling the gap in the current relative permeability models. The LB model proposed in this study is capable to simulate the complex physicochemical hydrate dissociation process. Considering the impacts of thermodynamic conditions (P,T), we investigated their influences on the coupled interaction between dissociation and seepage under three different morphologies and proposed a general permeability–saturation relationship. The results can be applied as input to adjust parameters in the continuum model, and provide instructions for exploring clean energy with environmental considerations.
Звіти організацій з теми "Generalized continuous media":
1
Bilovska, Natalia. HYPERTEXT: SYNTHESIS OF DISCRETE AND CONTINUOUS MEDIA MESSAGE. Ivan Franko National University of Lviv, March 2021. http://dx.doi.org/10.30970/vjo.2021.50.11104.
Анотація:
In the article we interpret discrete and continuous message as interrupted and constant, limited and continual text, which has specific features and a number of differences between traditional (one-dimensional) text and hypertext (multidimensional). The purpose of this study is to define the concept of “hypertext”, consideration of its characteristics and features of the structure, similarities and differences with the traditional text, including the message in the media and communication. To achieve the goal of the study, we used a number of methods typical of journalism. Empirical analysis enabled a generalized description of the subject of study, which allowed to know it as a phenomenon. With the help of generalization the characteristic and specific regularities and principles of hypertext were studied. The system method is used to identify the dependence of each element of hypertext on its place in the text system as a whole. The retrospective method helped to understand the preconditions for the emergence of hypertext, to trace the dynamics of its development. General scientific methods (analysis, synthesis, induction, deduction) made it possible to formulate the conclusions of the study. Thanks to hypertext and the hypertext systems, the concept of virtual reality has gained tangible meaning. In hypertext space, virtuality organically complements reality. The state of virtuality, in this case, becomes the concept of hyperreality, and all this merges into a single whole in the space of computer text. Due to its volume and multidimensionality, hypertext can arouse scientific interest as an interdisciplinary discipline. In today’s world, the phenomenon of hypertext has been the subject of numerous discussions, conferences and research in the field of social communications, linguistics and psychology. Today, a significant number of organizations conduct large-scale research based on the concepts of hypertext associations and associative navigation.