Dissipation Function Research Articles

Optimal synthesis of QCA logic circuit eliminating wire‐crossings

Wire-crossing plays a pivotal role toward the progress of non-complementary metal-oxide-semiconductor technology. Hefty amount of wire-crossings leads to many complications including cross-talk, colossal power dissipation and high cost function which in turn makes the fabrication difficult. In this regard, this work presents an efficient method for circuit implementation based on majority logic in quantum-dot cellular automata (QCA) with optimum wire-crossing. The authors' proposed method is able to eliminate wire-crossing by the generation and routing of proper intermediate function in the circuit utilising the orientation of the input variable. An algorithm to minimise the number of wire-crossing is also reported. Experimental results establish the effectiveness of the proposed method in circuit level also. Finally, a concrete framework to design a cost-effective logic circuit in QCA ensuring the least/optimum wire-crossing is established.

Chebyshev-like generalized Shapiro filters for high-accuracy flow computations

This paper presents Chebyshev-like generalized Shapiro (CS) filters with improved spectral-like resolution compared to existing generalized Shapiro filters. These new filters combine the advantages of Shapiro filters, i.e. arbitrary accuracy order, no-dispersion, full damping of 2Δ-waves, and the advantages of Chebyshev filters, i.e. purely dissipative response function with equal ripples satisfying an arbitrary Chebyshev criterion in passband. Thanks to the formalism of generalized Shapiro filters, general formulas are derived for arbitrary accuracy orders and arbitrary Chebyshev criterion. A python script is provided in appendix to compute CS filter coefficients. Computations based on the Euler equations assess the benefit of CS filters compared to the standard Shapiro filters. Since CS filters differ from Shapiro filters only by their coefficients, they can easily and advantageously be implemented in computational solvers already making use of generalized Shapiro filters.

Rock anelasticity due to patchy saturation and fabric heterogeneity: A double double‐porosity model of wave propagation

AbstractHeterogeneity of rock's fabric can induce heterogeneous distribution of immiscible fluids in natural reservoirs, since the lithological variations (mainly permeability) may affect fluid migration in geological time scales, resulting in patchy saturation of fluids. Therefore, fabric and saturation inhomogeneities both affect wave propagation. To model the wave effects (attenuation and velocity dispersion), we introduce a double double‐porosity model, where pores saturated with two different fluids overlap with pores having dissimilar compressibilities. The governing equations are derived by using Hamilton's principle based on the potential energy, kinetic energy, and dissipation functions, and the stiffness coefficients are determined by gedanken experiments, yielding one fast P wave and four slow Biot waves. Three examples are given, namely, muddy siltstones, clean dolomites, and tight sandstones, where fabric heterogeneities at three different spatial scales are analyzed in comparison with experimental data. In muddy siltstones, where intrapore clay and intergranular pores constitute a submicroscopic double‐porosity structure, wave anelasticity mainly occurs in the frequency range (104–107 Hz), while in pure dolomites with microscopic heterogeneity of grain contacts and tight sandstones with mesoscopic heterogeneity of less consolidated sands, it occurs at 103–107 Hz and 101–103 Hz (seismic band), respectively. The predicted maximum quality factor of the fast compressional wave for the sandstone is the lowest (approximately 8), and that of the dolomite is the highest. The results of the diffusive slow waves are affected by the strong friction effects between solids and fluids. The model describes wave propagation in patchy‐saturated rocks with fabric heterogeneity at different scales, and the relevant theoretical predictions agree well with the experimental data in fully and partially saturated rocks.

A Rayleighian approach for modeling kinetics of ionic transport in polymeric media.

We report a theoretical approach for analyzing impedance of ionic liquids (ILs) and charged polymers such as polymerized ionic liquids (PolyILs) within linear response. The approach is based on the Rayleigh dissipation function formalism, which provides a computational framework for a systematic study of various factors, including polymer dynamics, in affecting the impedance. We present an analytical expression for the impedance within linear response by constructing a one-dimensional model for ionic transport in ILs/PolyILs. This expression is used to extract mutual diffusion constants, the length scale of mutual diffusion, and thicknesses of a low-dielectric layer on the electrodes from the broadband dielectric spectroscopy measurements done for an IL and three PolyILs. Also, static dielectric permittivities of the IL and the PolyILs are determined. The extracted mutual diffusion constants are compared with the self-diffusion constants of ions measured using pulse field gradient (PFG) fluorine nuclear magnetic resonance (NMR). For the first time, excellent agreement between the diffusivities extracted from the Electrode Polarization spectra (EPS) of IL/PolyILs and those measured using the PFG-NMR are found, which allows the use of the EPS and the PFG-NMR techniques in a complimentary manner for a general understanding of the ionic transport.

An improved dissipative particle dynamics scheme

Dissipative particle dynamics (DPD) and smoothed dissipative particle dynamics (sDPD) have become most popular numerical techniques for simulating mesoscopic flow phenomena in fluid systems. Several DPD/sDPD simulations in the literature indicate that the model fluids should be designed with their dynamic response, measured by the Schmidt number, in a relevant range in order to reach a good agreement with the experimental results. In this paper, we propose a new dissipative weighting function (or a new kernel) for the DPD (or the sDPD) formulation, which allows both the viscosity and the Schmidt number to be independently specified as input parameters. We also show that some existing dissipative functions/kernels are special cases of the proposed one, and the imposed viscosity of the present DPD/sDPD system has a lower and upper limit. Numerical verification of the proposed function/kernel is conducted in viscometric flows.

Shear-thinning of molecular fluids in Couette flow

We use non-equilibrium molecular dynamics simulations, the Boltzmann equation, and continuum thermomechanics to investigate and characterize the shear-thinning behavior of molecular fluids undergoing Couette flow, interacting via a Lennard-Jones (LJ) potential. In particular, we study the shear-stress under steady-state conditions and its dependency on fluid density and applied shear-strain rate. Motivated by kinetic theory, we propose a rheological equation of state that fits observed system responses exceptionally well and captures the extreme shear-thinning effect. We notice that beyond a particular strain-rate threshold, the fluid exhibits shear-thinning, the degree of which is dependent on the density and temperature of the system. In addition, we obtain a shear-rate dependent model for the viscosity which matches the well established Cross viscosity model. We demonstrate how this model arises naturally from the Boltzmann equation and possesses an inherent scaling parameter that unifies the rheological properties of the LJ fluid. We compare our model with those in the literature. Finally, we formulate a dissipation function modeling the LJ fluid as a quasilinear fluid.

Resonant Oscillations of Non-Symmetrical Rotor with Mass Imbalance and Disk Skew

The non-symmetrical rotor with mass imbalance and disk skew has been considered. For full description of the rotor motion dynamic and mathematical models of the machine have been developed. Expressions for Lagrangian functions and Rayleigh dissipative function are formed. The motion equations are written as the Lagrangian equations of the second kind. By separation of variables the expressions of amplitude and phase of vibrations have been determined. The special emphasis is placed to the joint effect of mass imbalance and disk skew on the rotor dynamics which is observed over the whole range of shaft speed. The amplitudes of the vibrations near the critical speeds and residual phase angle depending on the generalized imbalance and the relative distance to the disk are studied. Detection of the residual phase angle at low rotation speeds is of practical importance, it is extremely important at balancing the rotor, since for determination of the mass eccentricity line the results of measurements at low speeds are used. The main working expressions are presented in a compact and non-dimensional form.

Some properties of the dissipative model of strain-gradient plasticity

A theoretical and computational investigation is carried out of a dissipative model of rate-independent strain-gradient plasticity and its regularisation. It is shown that the flow relation, when expressed in terms of the Cauchy stress, is necessarily global. The most convenient approach to formulating the flow relation is through the use of a dissipation function. It is shown, however, that the task of obtaining the dual version, in the form of a normality relation, is a complex one. A numerical investigation of problems in two space dimensions casts further light on the response using the dissipative theory in situations of non-proportional loading. The elastic gap, a feature reported in recent investigations, is observed in situations in which passivation has been imposed. The computational study indicates that the gap may be regarded as an efficient path between a load-deformation response corresponding to micro-free boundary conditions, and that corresponding to micro-hard boundary conditions, in which plastic strains are set equal to zero on all or part of the boundary.

Quasi-Static Linear Thermo-Viscoelastic Process with Irregular Viscous Dissipation

AbstractWe consider a mathematical model which describes the quasi-static evolution of a thermo-viscoelastic linear body with taking into account the effects of internal forces which generate a non linear viscous dissipative function. We derive a variational formulation of the system of equilibrium equation and energy equation. An existence result of weak solutions was obtained in an appropriate function space.

Phase transitions in tumor growth: IV relationship between metabolic rate and fractal dimension of human tumor cells

By the use of thermodynamics formalism of irreversible processes, complex systems theory and systems biology, it is derived a relationship between the production of entropy per unit time, the fractal dimension and the tumor growth rate for human tumors cells. The thermodynamics framework developed demonstrates that, the dissipation function is a Landau potential and also the Lyapunov function of the dynamical behavior of tumor growth, which indicate the directional character, stability and robustness of the phenomenon. The entropy production rate may be used as a quantitative index of the metastatic potential of tumors. The current theoretical framework will hopefully provide a better understanding of cancer and contribute to improvements in cancer treatment.

Non-monotonic Relaxation in a Harmonic Well

The dissipation function of Evans and Searles has its origins in describing entropy production, yet it has a straightforward dynamical interpretation as well. The ability to consider either dynamical or thermodynamical contexts deepens our understanding of the dissipation function as a concept, and of numerical results involving the dissipation function. One recent, important application of the dissipation function is in relaxation to equilibrium. Here we look at relaxation in a system of interacting molecules that are confined within a harmonic potential, undergoing Hamiltonian dynamics. We note some similarities, but also important differences, to previous studies. The dissipation function sheds light on the periodic return of our system towards its initial state. We find that intermolecular interactions play a much more significant role in the relaxation toward a non-uniform spatial distribution (induced by a conservative background field)than they do toward a uniform distribution, which is reflected in the strongly non-monotonic relaxation we observe. We also find that the maximum dissipation does not occur in the long-time limit, as one might expect of a relaxation process,but shortly after relaxation begins, beyond which a significant net overall decrease in the dissipation function is observed.

Energy dissipation of the liquid in systems with a hydrophobic surface

The work is divided into theoretical and experimental parts. In the theoretical part the viscous forces performance for both laminar as well as turbulent flow of compressible fluids are defined. It is split into the viscous forces useful power and the power corresponding to mechanical losses. This part is expressed by the dissipation function. It is shown that the dissipation function considering hydrophobic surfaces cannot be determined from the pressure difference. It is necessary to take into account the slip of the liquid over the hydrophobic surface which depends on the value of surface energy. The values of surface energy for different types of hydrophobic surfaces, obtained by experiment, are shown within this work. The new definition of the dissipation function for hydrophobic surfaces is presented depending on the adhesion coefficient, also determined by an experiment. The theoretical part of the work is complemented by experiment. The experiment is aimed at the differential pressure measurement in a circular cross section pipe. The results are processed for both laminar and turbulent stationary flow in relation to the flow. Both hydrophilic and hydrophobic surfaces and their mutual correlation are taken into consideration. On the basis of the new mathematical model for hydrophobic surfaces the value of dissipation function is determined depending on the slip velocity of the liquid along the hydrophobic surface.

Nonlinear dynamic analysis for coupled vehicle-bridge system with harmonic excitation

In this paper, a multi-degree-of-freedom lumped parameter coupled vehicle-bridge dynamic model is proposed considering the nonlinearities of suspension and tire stiffness/damping and the nonlinear foundation of bridge. In terms of modelling, the continuous expressions of the kinetic energy, potential energy and the dissipation function are constructed. The dynamic equations of the coupled vehicle-bridge system (CVBS) are derived and discretized using Galerkin’s scheme, which yield a set of second-order nonlinear ordinary differential equations with coupled terms. The numerical simulations are conducted by using the Newmark-β integration method to perform a parametric study of the effects on excitation amplitude, suspension stiffness and position relation. The bifurcation diagram, 3-D frequency spectrum and largest Lyapunov exponent are demonstrated in order to better understand the vibration properties and interaction between the vehicle and bridge with the key system parameters. It can be found that the nonlinear dynamic characteristics such as parametric resonance, jump phenomena, periodic, quasi-periodic and chaotic motions are strongly attributed to the interaction between vehicle and bridge. Significantly, under the combined internal and external excitations, the vibration amplitudes of the CVBS have a certain degree of dependence on the external excitation. Suspension stiffness could lead to complex dynamics such as the higher-order bifurcations increase and the chaotic regions broaden. The increasing of distance could effectively control the nonlinear vibration of CVBS. The application of the proposed nonlinear coupled vehicle-bridge model would bring higher computational accuracy and make it possible to design the vehicle and bridge simultaneously.

Viscoelastic tides: models for use in Celestial Mechanics

This paper contains equations for the motion of linear viscoelastic bodies interacting under gravity. The equations are fully three dimensional and allow for the integration of the spin, the orbit, and the deformation of each body. The goal is to present good models for the tidal forces that take into account the possibly different rheology of each body. The equations are obtained within a finite dimension Lagrangian framework with dissipation function. The main contribution is a procedure to associate to each spring–dashpot model, which defines the rheology of a body, a potential and a dissipation function for the body deformation variables. The theory is applied to the Earth (solid part plus oceans) and a comparison between model and observation of the following quantities is made: norm of the Love numbers, rate of tidal energy dissipation, Chandler period, and Earth–Moon distance increase.

A thermodynamic consistent rate-dependent elastoplastic-damage model

In this article, a rate-dependent elastoplastic-damage constitutive model considering the effect of strain rate has been developed. The derivation of this model has been established based on the irreversible thermodynamics with internal variables within the fundamentals of Continuum damage mechanics (CDM). For investigating the rate effect, an additional power function dependent on the effective strain rate has been involved in the plastic dissipation function (dynamic plastic yield surface). The damage has been assumed as a tensor-type variable and based on the energy equivalence hypothesis, the damage evolution has been developed. The proposed constitutive model has been implemented into user-defined subroutines UMAT and VUMAT in the finite-element program ABAQUS/(Standard and Explicit). For this purpose, the implicit and explicit stress integration algorithms of the model have been explained. The model has been validated by comparing the predicted results with experimental data conducted on Al2024-T3. These experiments are including the tensile and double-notched tests. Furthermore, the numerical results have been compared with some data available in the literature. The numerical examples show the excellent correlation between experiments and simulations for stress (or force) and damage results.

Nonlinear analysis of a parametrically excited beam with intermediate support by using Multi-dimensional incremental harmonic balance method

In this paper, a nonlinear Euler-Bernoulli beam under a concentrated harmonic excitation with intermediate nonlinear support is investigated. Continuous expression for the kinetic energy, potential energy and dissipation function are constructed. An energy method based on the Lagrange equation combined with the Galerkin truncation is used for discretizing the governing equation. The Multi-dimensional incremental harmonic balance method (MIHBM) is derived, and the comparisons between the numerical results and the approximate analytical solutions based on the MIHBM verify the excellent accuracy of the MIHBM. The steady state dynamic of the beam is investigated by MIHBM. In order to investigate the energy transmission and understand the vibration response of the Euler-Bernoulli beam, the effects of the key parameters on the dynamic behaviors are studied and discussed, individually. The results show that the amplitude-frequency curves exhibits softening nonlinear behavior in the super-harmonic resonance region, and near resonant region the hardening nonlinear behavior is observed depending on the different parameters. Nonlinear dynamic analysis, such as bifurcation, 3-D frequency spectrum, waveform, frequency spectrum, phase diagram and Poincaré map, are also presented in order to study the influences of the key parameters on the vibration behaviors for the beam in a more accurate manner. In addition, the path to chaotic motion is observed to be through a sequence of the periodic motion and quasi-periodic motion.

Thermodynamic Optimization of an Electric Circuit as a Non-steady Energy Converter

Abstract Electric circuits with transient elements can be good examples of systems where non-steady irreversible processes occur; so in the same way as a steady-state energy converter, we use the formal construction of the first-order irreversible thermodynamic to describe the energetics of these circuits. In this case, we propose an isothermal model of two meshes with transient and passive elements, besides containing two voltage sources (which can be functions of time); this is a non-steady energy converter model. Through the Kirchhoff equations, we can write the circuit phenomenological equations. Then, we apply an integral transformation to linearize the dynamic equations and rewrite them in algebraic form, but in the frequency space. However, the same symmetry for steady states appears (cross effects). Thus, we can study the energetic performance of this converter model by means of two parameters: the “force ratio” and the “coupling degree”. Furthermore, it is possible to obtain characteristic functions (dissipation function, power output, efficiency, etc.). They allow us to establish a simple optimal operation regime of this energy converter. As an example, we obtain the converter behavior for the maximum efficient power regime.

Estimating the dissipative factors of synaptic exocytosis in Drosophila using a filter based reverse engineering method

The SNARE-regulated exocytosis is an important molecular level mechanism for the persistent inter-neuronal communication via plasticity of neurons. Without considering the dissipation of synaptic vesicle, the explanation of the inter-neuronal communication via plasticity of neurons in existing models cannot fully account for the persistence of neuronal plasticity. In this paper the dissipative factors CPX and SYT corresponding to unbinding neurotransmitters fused with the membrane are estimated using a reverse engineering method where the dynamic flux is embedded in the filtering model of synaptic transmission. With the CPX and SYT in the corresponding regulation mechanism of exocytosis being estimated, the dissipation function of synaptic vesicle for the persistence of neuronal plasticity is explicitly expressed.

Biomechanical Design of Elastic Protein Biomaterials: A Balance of Protein Structure and Conformational Disorder.

Elastic biomaterials are found across biology where they fulfill diverse load-bearing and energy storage and dissipation functions. This class of biomaterials comprises elastic proteins that provide materials with combinations of extensibility, stiffness, tensile strength, toughness, and viscoelastic properties. Differences in mechanical properties are due in large part to variations in the ratio of secondary structure and conformational disorder of constituent protein monomers, arising from differences in amino acid sequence. This natural diversity provides rich inspiration for the design of elastic biomaterials. Here, we review the relationship between sequence, structure, disorder, and mechanical properties of elastic proteins from natural materials ranging from highly extensible and soft, to mechanically strong and tough. We describe molecular strategies as well as recombinant efforts to design materials with tailored mechanical properties, with the ultimate aim of rationally engineering biomaterials for advanced biomedical applications.

Propagation of Love waves in a prestressed Voigt-type viscoelastic orthotropic functionally graded layer over a porous half-space

The present paper investigates the theory of propagation of Voigt-type viscoelastic Love waves in a functionally graded material layer over an anisotropic porous half-space. The complex dispersion equation of Love waves has been expanded into real and imaginary parts. An assumption of the dissipation factor has been applied. Some particular cases have also been deduced, and it is noticed that the dispersion equation is in well agreement with the classical Love wave equation. In addition, to study the effect of initially stressed parameter, inhomogeneity parameter and porosity on phase velocity and dissipation function, some significant observations have been made by detailed numerical calculations and illustrated graphically. The results of this paper may present a deeper insight into the nature of the propagation behavior in elastic inhomogeneous functionally graded materials and can provide theoretical guidance for the design and optimization to the field of earthquake engineering.