Maxwell Type Research Articles

J0550402 修正Maxwell型反射モデルを用いた平行平板間流れのモンテカルロシミュレーション([J055-04]マイクロ・ナノスケール熱流体現象(4))

Modified Maxwell type reflection model which incorporated two accommodation coefficients for the probability of the diffuse reflection α_n and α_l, for molecular velocities normal to and parallel to the wall was applied to the was applied to the Monte Carlo simulation of rarefied gas flows between parallel flat plates and comparing with simulation data yielded by the Cercignani-Lampis-Lord (CLL) reflection model. The profiles of velocity and heat flux distribution were in good agreement with those of CLL model. However there were some discrepancies in the temperature and density distribution between two models.

Ultrasonic propagation in suspensions of encapsulated compressible nanoparticles

Dispersion and absorption are examined for dilute suspensions of encapsulated droplets of nanometric size, with typical radii around 100 nm. This new generation of contrast agents is designed for targeted delivery of drugs. Compared to standard contrast agents used for imaging, particles are of smaller size to pass the endothelial barrier, their shell made up of biocompatible material is stiffer to undergo a longer time life and they have a liquid (PFC) instead of a gaseous core. Ultrasound propagation of these suspensions is modeled by combining (i) a dilatational mode of oscillation assuming a compressible shell with a visco-elastic behavior of Kelvin-Voigt or Maxwell type (relaxation), (ii) a translational mode of oscillation induced by visco-inertial interaction with the ambient fluid, and (iii) polydispersion in terms of radius and shell thickness. Influence of the various effects will be examined. Experimental measurements of the dispersion and absorption properties of nanodroplets solutions over the 1–100 MHz frequency range are performed for various temperatures and concentrations. They allow to fit with good accuracy the model properties and estimate some unknown mechanical properties of the shell of the nanodroplets. [Work supported by programme Emergence-UPMC—project NACUNAT and by Inserm/Plan Cancer—project NABUCCO.]

Mathematical Foundations of the Classical Maxwell-Lorentz Electrodynamic Models in the Canonical Lagrangian and Hamiltonian Formalisms

We present new mathematical foundations of classical Maxwell-Lorentz electrodynamic models and related charged particles interaction-radiation problems, and analyze the fundamental least action principles via canonical Lagrangian and Hamiltonian formalisms. The corresponding electrodynamic vacuum field theory as- pects of the classical Maxwell-Lorentz theory are ana- lyzed in detail. Electrodynamic models of charged point particle dynamics based on a Maxwell type vacuum field medium description are described, and new field theory concepts related to the mass particle paradigms are dis- cussed. We also revisit and reanalyze the mathematical structure of the classical Lorentz force expression with respect to arbitrary inertial reference frames and present new interpretations of some classical special relativity theory relationships.

ON MODELS FOR VISCOELASTIC MATERIALS THAT ARE MECHANICALLY INCOMPRESSIBLE AND THERMALLY COMPRESSIBLE OR EXPANSIBLE AND THEIR OBERBECK–BOUSSINESQ TYPE APPROXIMATIONS

Viscoelastic fluid like materials that are mechanically incompressible but are compressible or expansible with respect to thermal stimuli are of interest in various applications ranging from geophysics and polymer processing to glass manufacturing. Here we develop a thermodynamical framework for the modeling of such materials. First we illustrate the basic ideas in the simpler case of a viscous fluid, and after that we use the notion of natural configuration and the concept of the maximization of the entropy production, and we develop a model for a Maxwell type viscoelastic fluid that is mechanically incompressible and thermally expansible or compressible.An important approximation in fluid mechanics that is frequently used in modeling buoyancy driven flows is the Oberbeck–Boussinesq approximation. Originally, the approximation was used for studying the flows of viscous fluids in thin layers subject to a small temperature gradient. However, the approximation has been used almost without any justification even for flows of non-Newtonian fluids induced by strong temperature gradients in thick layers. Having a full system of the governing equations for a Maxwell type viscoelastic mechanically incompressible and thermally expansible or compressible fluid, we investigate the validity of the Oberbeck–Boussinesq type approximation for flows of this type of fluids. It turns out that the Oberbeck–Boussinesq type approximation is in general not a good approximation, in particular if one considers "high Rayleigh number" flows. This indicates that the Oberbeck–Boussinesq type approximation should not be used routinely for all buoyancy driven flows, and its validity should be thoroughly examined before it is used as a mathematical model.

Viscoelastic Properties of Poly(vinyl alcohol) Hydrogels Having Permanent and Transient Cross-Links Studied by Microrheology, Classical Rheometry, and Dynamic Light Scattering

Dynamics of poly(vinyl alcohol) (PVA) hydrogels having chemical and physical transient cross-links simultaneously (dual cross-link PVA gels) were studied by microrheology based on diffusing-wave spectroscopy (DWS), classical rheology and single dynamic light scattering (DLS), and compared with those of corresponding chemical and physical PVA gels. Three different relaxation modes (fast, intermediate and slow modes) are observed for physical gels, while one mode (fast mode) is found for chemical gels, and two (fast and intermediate) for dual cross-link gels. The three modes are attributed respectively to Brownian diffusion of PVA polymer or collective diffusion of the network or gel mode (fast mode), macroscopic stress relaxation (intermediate mode whose characteristic time shows q0 dependence) and Brownian diffusion of aggregates (slow mode). Microrheological measurements are in good agreement with macrorheological showing segmental Rouse mode dynamics in the high frequency range. For physical gels, we found Maxwell type viscoelasticity characterized by a crossover frequency (maximum of G″) and G′ ∼ ω2 and G″ ∼ ω1 in the lower frequency range. The chemical gels displayed an elastic plateau with low G″ at low frequency. For the dual cross-link gel a maximum of G″ was observed, and its characteristic time agrees with that of the intermediate mode measured by DLS. We show that this relaxation mode corresponds to the associative Rouse mode characterized by G′ = G″ ∼ ω0.5, depending on the dissociation rate of the reversible transient cross-links. We propose a stress relaxation mechanism of the PVA chains in the presence of elastically inactive but associative transient cross-links which induces incomplete stress relaxation.

Influence of Ni2+ substitution on the structural, dielectric and magnetic properties of Cu–Cd ferrite nanoparticles

Nanoparticles with compositions of Cu0.4−0.5xCd0.2Ni0.4+xFe2−0.5xO4 (0.0⩽x⩽0.5) were successfully synthesized by a citrate–nitrate sol–gel auto combustion route. The combusted powder was calcinated at four hours in a furnace and then slowly cooled to room temperature. The analysis methods of FTIR, XRD, FESEM, VSM and dielectric measurements were used to characterize prepared magnetic particles. The effect of Ni2+ substitution on structural, magnetic and dielectric properties of Cu–Cd ferrite nanoparticles was studied. The comprehensive studies on compositional and frequency dependent dielectric properties were carried out by means of AC conductivity (σac), imaginary dielectric constant (ε′′), loss tangent (tanδ), impedance and dielectric modulus (real and imaginary) measurements in frequency range of 50Hz–5MHz at room temperature. The structural properties investigated by using X-ray diffraction, scanning electron microscopy, and Fourier transform infrared spectroscopy. X-ray diffraction pattern and FTIR results revealed that synthesized samples are in single phase. It is observed that the dielectric constant (ε′′) and dielectric loss (tanδ) value decreases with increase in Ni2+ concentration (x). At low frequency the Maxwell type interfacial polarization was observed. Magnetization measurement shows that the Curie temperature of the samples increases with Ni2+ concentration, which is explained by a change in the A–O–B super exchange interaction.

J053032 希薄気体流れの解析における複数の適応係数を有するMaxwell型反射モデルの性能(〔J053-03〕マイクロ・ナノスケールの熱流体現象(3))

Maxwell type reflection model with multi accommodation coefficients was applied to the Monte Carlo simulation of two dimensional rarefied gas flows around a flat plate and comparing with experimental data and simulation data yielded by the Cercignani-Lampis-Lord (CLL) reflection model. The profiles of rotational temperature and rotational energy distribution near the plate were in reasonable agreement with those of experiment and CLL model.

Viscoelastic foundation analysis of Single Cantilevered Beam (SCB) test under stationary loading

Abstract A simple, Maxwell type foundation model has been derived for analysis of the Single Cantilever Beam (SCB) fracture test, used for evaluating adhesively bonded joints under stationary loading conditions. Crack initiation tests, under constant force loading, are presented to introduce the effective λ eff concept, which can be extended to the wedge test configuration ( viz. constant deflection/relaxation loading). A simple Maxwell model is used to approximate relaxation/creep behaviour of the bondline. Analytical solutions are found in the Laplace domain. Numerical inversion techniques are proposed to calculate the evolution of macroscopic quantities, such as deflection or applied force, but also stress and strain along the bondline. This analysis gives some insight into the crack nucleation process and indications for better prediction of threshold values for ‘infinite life’ (no crack initiation).

A model for ultrasound absorption and dispersion in dilute suspensions of nanometric contrast agents

Ultrasound dispersion and absorption are examined in dilute suspensions of contrast agents of nanometric size, with a typical radius around 100 nm. These kinds of contrast agents are designed for targeted delivery of drugs for cancer treatment. Compared to standard contrast agents used for imaging, particles are of smaller size to pass through the endothelial barrier, their shell, made up of biocompatible polymer, is stiffer to undergo a longer lifetime, and they have a liquid core instead of a gaseous one. Ultrasound propagation in dilute suspension is modeled by combining two modes for particle oscillations. The first one is a dilatational mode assuming an incompressible shell with a rheological behavior of Kelvin-Voigt or Maxwell type. The second one is a translational mode induced by visco-inertial interaction with the ambient fluid. The relative importance of these two modes of interaction on both dispersion and absorption is quantified and analyzed for a model system and for two radii (75 and 150 nm) and the two rheological models. The influence of shell parameters (Young modulus, viscosity, and relative thickness) is finally discussed.

On the direct connection of rheological elements in nonlinear continuum mechanics

AbstractThe structure of complicated phenomenological material models at finite strains is often exemplified with the help of rheological elements. Thereby, simple material behaviour, i.e. elasticity or viscous and plastic flow, are composes by components. In our approach, we directly apply this concept to obtain material models at finite strains. Towards this end, the thermodynamically consistent material behaviour of single elements is defined first. Subsequently, the elements are connected by evaluation of stress equilibria equations formulated on interconnecting configurations. The basic equations of this concept are presented using the example of nonlinear viscoelasticity of Maxwell type. The model results from a series connection of an elastic and a viscous element, whereas both are formulated in a thermodynamically consistent way within the framework on nonlinear continuum mechanics. Furthermore, an approach of numerical implementation using the stress equilibria is suggested. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Four-Dimensional Maxwell Equation for Social Processes in Web-Based Learning and Teaching

This paper describes how the principal structure of a system of equations fundamental to science, namely the Maxwell equations governing electromagnetism, could be analogously applied to social procedures among humans who start to create emerging networks through gaming. Inspired by a cartographic windrose, a new type of notation for social procedures is introduced that allows to graphically depict “information”, “team”, “debate”, “integration” as four basic dimensions; symbolically called soprano, alto, tenor and bass. Experiences with a web-based role-play (“Surfing Global Change”) show that these four basic dimensions tend to peak one after the other along a suitably designed gaming procedure. The resulting sequence of the “voices” S, T, A, B gives rise to hypothesizing a general pattern of social behavior that qualitatively could formally be described by a four-dimensional Maxwell type set of equations of these four variables. It is hypothesized that in analogy to an electromagnetic wave also a social process of harmonious flow in S, T, A, B might emerge that describes suitable and successful conditions for game play and game-based learning.

The Lagrangian and Hamiltonian Aspects of the Electrodynamic Vacuum-Field Theory Models

The important classical Ampere’s and Lorentz laws derivations are revisited and their relationships with the modern vacuum field theory approach to modern relativistic electrodynamics are demonstrated. The relativistic models of the vacuum field medium and charged point particle dynamics as well as related classical electrodynamics problems jointly with the fundamental principles, characterizing the electrodynamical vacuum-field structure, based on the developed field theory concepts are reviewed and analyzed detail. There is also described a new approach to the classical Maxwell theory based on the derived and newly interpreted basic equations making use of the vacuum field theory approach. There are obtained the main classical special relativity theory relationships and their new explanations. The well known Feynman approach to Maxwell electromagnetic equations and the Lorentz type force derivation is also. A related charged point particle dynamics and a hadronic string model analysis is also presented. We also revisited and reanalyzed the classical Lorentz force expression in arbitrary non-inertial reference frames and present some new interpretations of the relations between special relativity theory and its quantum mechanical aspects. Some results related with the charge particle radiation problem and the magnetic potential topological aspects are discussed. The electromagnetic Dirac-Fock-Podolsky problem of the Maxwell and Yang-Mills type dynamical systems is analyzed within the classical Dirac-Marsden-Weinstein symplectic reduction theory. Based on the Gelfand-Vilenkin representation theory of infinite dimensional groups and the Goldin-Menikoff-Sharp theory of generating Bogolubov type functionals the problem of constructing Fock type representations and retrieving their creation-annihilation operator structure is analyzed. An application of the suitable current algebra representation to describing the non-relativistic Aharonov-Bohm paradox is demonstrated. The current algebra coherent functional representations are constructed and their importance subject to the linearization problem of nonlinear dynamical systems in Hilbert spaces is also presented.

J053015 壁面温度勾配に誘起される希薄気体流れのモンテカルロシミュレーション

Two dimensional rarefied gas flows in the free molecular limit between parallel flat plates with sinusoidal temperature distribution were simulated by the direct simulation Monte Carlo method. A Maxwell type reflection model which incorporated two accommodation coefficients for the ratio of the diffuse reflection to the specular reflection an and a,, for molecular velocities normal to and parallel to the wall was applied to the boundary condition of the plates. Three types of flows such as combinations of vortical flows and creep flows along a surface were simulated according to the set of two accommodation coefficients a,and a.

Diffuse interface model for compressible fluid – Compressible elastic–plastic solid interaction

An Eulerian hyperbolic diffuse interface model for elastic–plastic solid–fluid interaction is constructed. The system of governing equations couples Euler equations of compressible fluids and a visco-plastic model of Maxwell type materials (the deviatoric part of the stress tensor decreases during plastic deformations) in the same manner as models of multicomponent fluids. In particular, the model is able to create interfaces which were not present initially.The model is thermodynamically compatible: it verifies the entropy inequality. However, a numerical treatment of the model is particularly challenging. Indeed, the model is non-conservative, so a special numerical splitting is proposed to overcome this difficulty. The numerical algorithm contains two relaxation procedures. One of them is physical and is related to the plastic relaxation mechanism (relaxation toward the yield surface). The second one is numerical. It consists in replacing the algebraic equation expressing a mechanical equilibrium between components by a partial differential equation with a short relaxation time. The numerical method was tested in 1D case (Wilkins’ flying plate problem), 2D plane case (impact of a projectile on a plate) and axisymmetrical case (Taylor test problem, impact with penetration effects, etc.). Numerical examples show the ability of the model to deal with real physical phenomena.

Abraham-Lorentz-Dirac equation in 5D Stuekelberg electrodynamics

We derive the Abraham-Lorentz-Dirac (ALD) equation in the framework of the electrodynamic theory associated with Stueckelberg manifestly covariant canonical mechanics. In this framework, a particle worldline is traced out through the evolution of an event xμ (τ). By admitting unconstrained commutation relations between the positions and velocities, the associated electromagnetic gauge fields are in general dependent on the parameter τ, which plays the role of time in Newtonian mechanics. Standard Maxwell theory emerges from this system as a τ-independent equilibrium limit. In this paper, we calculate the τ-dependent field induced by an arbitrarily evolving event, and study the long-range radiation part, which is seen to be an on-shell plane wave of the Maxwell type. Following Dirac's method, we obtain an expression for the finite part of the self-interaction, which leads to the ALD equation that generalizes the Lorentz force. This third-order differential equation is then converted to an integro-differential equation, identical to the standard Maxwell expression, except for the τ-dependence of the field. By studying this τ-dependence in detail, we show that field can be removed from the integration, so that the Lorentz force depends only on the instantaneous external field and an integral over dynamical variables of the event evolution. In this form, pre-acceleration of the event by future values of the field is not present.

Dynamics of shock waves in elastic-plastic solids

The Maxwell type elastic-plastic solids are characterized by decaying the absolute values of the principal components of the deviatoric part of the stress tensor during the plastic relaxation step. We propose a mathematical formulation of such a model which is compatible with the von Mises criterion of plasticity. Numerical examples show the ability of the model to deal with complex physical phenomena.

Finite motions from periodic frameworks with added symmetry

Recent work from authors across disciplines has made substantial contributions to counting rules (Maxwell type theorems) which predict when an infinite periodic structure would be rigid or flexible while preserving the periodic pattern, as an engineering type framework, or equivalently, as an idealized molecular framework. Other work has shown that for finite frameworks, introducing symmetry modifies the previous general counts, and under some circumstances this symmetrized Maxwell type count can predict added finite flexibility in the structure. In this paper we combine these approaches to present new Maxwell type counts for the columns and rows of a modified orbit matrix for structures that have both a periodic structure and additional symmetry within the periodic cells. In a number of cases, this count for the combined group of symmetry operations demonstrates there is added finite flexibility in what would have been rigid when realized without the symmetry. Given that many crystal structures have these added symmetries, and that their flexibility may be key to their physical and chemical properties, we present a summary of the results as a way to generate further developments of both a practical and theoretic interest.

Equations of Maxwell type

For an elliptic complex of first order differential operators on a smooth manifold X , we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to that of classical Maxwell's equations. The paper focuses on boundary value problems for the abstract Maxwell equations, especially on the Cauchy problem.

The Effect of Mass Ratio and Air Damper Characteristics on the Resonant Response of an Air Damped Dynamic Vibration Absorber

In this paper, it is shown that, a road vehicle 2DOF air damped quartercar suspension system can conveniently be transformed into a 2DOF air damped vibrating system representing an air damped dynamic vibration absorber (DVA) with an appropriate change in the ratio µ of the main mass and the absorber mass i.e. when mass ratio µ >> 1. Also the effect of variation of the mass ratio, air damping ratio and air spring rate ratio, on the motion transmissibility at the resonant frequency of the main mass of the DVA has been dis- cussed. It is shown that, as the air damping ratio in the absorber system increases, there is a substantial decrease in the motion transmissibility of the main mass system where the air damper has been modeled as a Maxwell type. Optimal value of the air damping ratio for the minimum motion transmissibility of the main mass of the system has been determined. An experimental setup has been designed and developed with a control system to vary air pressure in the damper in the absorber system. The motion transmissibility characteristics of the main mass system have been obtained, and the optimal value of the air damping ratio has been determined for minimum motion transmissibility of the main mass of the system

OPTIMUM DESIGN FOR STRUCTURAL SYSTEM WITH MAXWELL TYPE VISCOUS DAMPER BASED ON STOCHASTICALLY EQUIVALENT DAMPING FACTOR

The purpose of this study is to evaluate the optimum damping coefficients of Maxwell type viscous dampers which maximize the damping factor of a structural system. The damping factor is stochastically estimated based on the energy response of the structural system under a white noise excitation. It is found that the optimum distribution of the non-dimensional damping coefficients is nearly proportional to that of stiffness coefficients of Maxwell type damper elements. The approximate distribution model is also proposed based on this finding. The effectiveness of the optimized damping system is then demonstrated through the response analysis for several observed earthquake excitations.