Link between Continuous and Discrete Descriptions of Noise in Nonlinear Resistive Electrical Components

This article investigates spatiotemporally discrete or continuous stochastic descriptions, where we focus on differences in heat naturally defined between the particle level and the density field. Both descriptions are found to generally make the heat differences by the entropic term expressed just with the number density through spatial projection from the many particles' positions onto the density field. The transformation from the Langevin to Dean-Kawasaki equationsis considered as the projection in the continuous descriptions, where the emergent heat differences undergo little temporal variations due to the sparse distributions of the point particles. On the other hand, the analogous formalisms constructed in the discrete models may exhibit the explicit temporal evolutions of the entropic term. Furthermore, we develop arguments about the interpretation and applicability of the heat differences as well as the perspectives to a many-polymer system.

A general scheme to patch together discrete and continuous descriptions of diffusion within the same physical space is studied. In the discrete description, diffusion is described by microscopic random walkers on a lattice; in the continuous description, diffusion is described through the macroscopic diffusion equation. The coupling scheme is based on the mutual exchange of mass flux across the discrete-continuous interface. Detailed tests of the scheme, coupling particle, and field descriptions are particularly illustrative for the diffusion problem. Both the nonequilibrium transport behavior and the equilibrium fluctuations of the combined discrete-continuous system are in agreement with theoretical predictions.

Quality Control (QC) procedures are mandatory to achieve accuracy in radiotherapy treatments. For that purpose, classical methods generally use physical phantoms that are acquired by the system in place of the patient. In this paper, the use of digital test objects (DTO) replace the actual acquisition¹. A DTO is a 3D scene description composed of simple and complex shapes from which discrete descriptions can be obtained. For QC needs, both the DICOM format (for Treatment Planning System (TPS) inputs) as well as continuous descriptions are required. The aim of this work is to define an equivalence model between a continuous description of the three dimensional (3D) scene used to define the DTO, and the DTO characteristics. The purpose is to have an XML- DTO description in order to compute discrete calculations from a continuous description. The defined structure allows also to obtain the three dimensional matrix of the DTO and then the series of slices stored in the DICOM format. Thus, it is shown how possibly design DTO for quality control in CT simulation and dosimetry.

The effect of bow-bulbs on reduction of wave resistance is studied through some kinds of experiment with wedge models and a ship model of fine hull form. The stress is focused on their effects on wave configuration and flow velocities in the near-field. The effect of frame-lines of hull forms on both linear and nonlinear wave resistance components is also studied with a ship model of fine practical hull form. An approximate method of estimating the two resistance components is proposed and applied to hull form improvement.

Ferroresonance is a phenomenon that arises because it is triggered by a transient condition such as a switching, lightning strike, or short circuit disturbance. This phenomenon produced an abnormal form of voltage and overcurrent. It is caused by a non-linear inductance component (L), resistance component (R) and the capacitance (C) is constant in a system. In this study, the design and implementation of a ferroresonance test module on a low-voltage 3-phase transformer are made to physically analyze the small-scale ferroresonance phenomenon based on conditions in the system/field. The test results show that the design of the test module that is made can function correctly. The test module can produce a ferroresonance response in a 3-phase transformer with H and M cores. H and M cores are types of iron cores from the transformer used in this study. The test is carried out by increasing the power supply voltage until it reaches the transformer voltage rating and then varying the phase discharge and capacitor value to raise a ferroresonance response. The phased release variation is the release of 1 phase and 2 phases with capacitors variations of 10µF, 20 µF, and 30µF in series and series-parallel configurations. The ferroresonance response of the voltage wave obtained in the series-parallel configuration produced a more distorted wave than the series. Based on the test results, when testing with various capacitors, the greater the value of the capacitor, the greater the voltage required to generate the ferroresonance response, and Cseries has a more dominant influence than Cparallel. It takes a more significant value of the series capacitor (Cseries) to reduce the power supply voltage needed to get a ferroresonance response with a decrease of up to 28%.

The relation between the continuous and the discrete: A note on the first principles of speech dynamics

Optimization of energy supply systems with simulated annealing: continuous and discrete descriptions

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain from the microscopic domain, meanwhile, dynamically couple discrete and continuum descriptions. Our main strategy is to construct the total energy functional of a charge transport system to encompass the polar and nonpolar free energies of solvation, and chemical potential related energy. By using the Euler-Lagrange variation, coupled Laplace-Beltrami and Poisson-Nernst-Planck (LB-PNP) equations are derived. The solution of the LB-PNP equations leads to the minimization of the total free energy, and explicit profiles of electrostatic potential and densities of charge species. To further reduce the computational complexity, the Boltzmann distribution obtained from the Poisson-Boltzmann (PB) equation is utilized to represent the densities of certain charge species so as to avoid the computationally expensive solution of some Nernst-Planck (NP) equations. Consequently, the coupled Laplace-Beltrami and Poisson-Boltzmann-Nernst-Planck (LB-PBNP) equations are proposed for charge transport in heterogeneous systems. A major emphasis of the present formulation is the consistency between equilibrium LB-PB theory and non-equilibrium LB-PNP theory at equilibrium. Another major emphasis is the capability of the reduced LB-PBNP model to fully recover the prediction of the LB-PNP model at non-equilibrium settings. To account for the fluid impact on the charge transport, we derive coupled Laplace-Beltrami, Poisson-Nernst-Planck and Navier-Stokes equations from the variational principle for chemo-electro-fluid systems. A number of computational algorithms is developed to implement the proposed new variational multiscale models in an efficient manner. A set of ten protein molecules and a realistic ion channel, Gramicidin A, are employed to confirm the consistency and verify the capability. Extensive numerical experiment is designed to validate the proposed variational multiscale models. A good quantitative agreement between our model prediction and the experimental measurement of current-voltage curves is observed for the Gramicidin A channel transport. This paper also provides a brief review of the field.

We first examine the discrete case in its simplest form, a one-dimensional lattice-a linear chain-in which a cell at each site comprises only one ‘atom’ of mass m (Fig. 2.1). Each of these atoms-not to be mistaken for the real atoms of atomic physics-is a point-like mass, without internal structure, subject to interactions with all other atoms in the chain, but more significantly with its nearest neighbours. The first question raised, therefore, is about the modelling of these interactions, which must be consistent with known facts, e.g. the macroscopically observable elasticity of perfect crystals. On the other hand, the interactions are such that a typical interatomic potential V (Fig. 2.2a) is attractive at relatively large distances and repulsive at short distances, with the equilibrium at the binding energy. The binding energy is a characteristic feature of a specific crystal. The force f acting between the ‘atoms’ is the derivative (V’) of V. Figure 2.2 shows both V (with respect to separation R binding potential) and f The force/max is the maximum force that the pair can sustain, corresponding.

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

Flow through geothermal reservoirs is highly complex, and often includes contributions from both fracture networks and the porous rock matrix. Discrete Fracture Network (DFN) models are proven, effective tools for the characterization of rock masses especially where fracture dominated fluid flow is encountered; whereas more conventional tools, such as Finite Volume (FV) methods, are more numerically favorable for simulating problems where detailed multiphysics is required. This paper presents a workflow that combines discrete and continuum descriptions that captures the salient features of the geological materials whilst also remaining numerically tractable. DFN models of fractured rock masses are typically developed using statistical distributions to generate realistic three-dimensional (3D) descriptions of the natural fracture network. Superimposed with this fracture description, is a matrix-orientated description based on an intact rock property model. Integration of these two descriptions into a single continuum rock mass description is achieved through a novel discrete-continuum upscaling process which combines fractures and intact properties into a unified form, providing effective mass permeability and geomechanical descriptions. The composite rock mass description is then carried forward into a numerically efficient multiphysics solver that provides effective simulation of both temperature and flow in a fully coupled manner to evaluate the performance potential of geothermal reservoir units. In addition, it will be demonstrated how the presented work can naturally embed within the stochastic framework of DFN and permit a probabilistic based evaluation. This paper presents application of the hybrid DFN-FV workflow for a hot sedimentary aquifer. The application is presented in terms of the characterization steps and a description of the input used, which is then supplemented with the dual fracture and matrix description. The demonstration will also touch on the efficient gridding of geological domains and provide example simulation results of multi-well injector and producer fluid flow and heat transfer. The work in this paper shows how the DFN-FV approach can be systematically employed to help with the success of geothermal well placement and completion studies in hot sedimentary aquifers.

From Discrete to Continuum Models of Three-Dimensional Deformations in Epithelial Sheets

Media composed of colliding hard disks (2D) or hard spheres (3D) serve as good approximations for the collective hydrodynamic description of gases, liquids and granular media. In the present study, the compressible hydrodynamics and shock dynamics are studied for a two-dimensional hard-disk medium at both the continuum and discrete particle level descriptions. For the continuum description, closed form analytical expressions for the inviscid hydrodynamic description, shock Hugoniot, isentropic exponent and shock jump conditions were obtained using the Helfand equation of state. The closed-form analytical solutions permitted us to gain physical insight into the role of the material’s density on its compressibility, i.e. how the medium compresses under mechanical loadings and sustains wave motion. Furthermore, the predictions were found in excellent agreement with calculations using the event driven molecular dynamics method involving 30,000 particles over the entire range of compressibility spanning the dilute ideal gas and liquid phases. In all cases, it was found that the energy imparted by the piston motion to the thermalized medium behind the propagating shock was quasi-independent of the medium’s packing fraction, with a correction vanishing with increasing shock Mach numbers.

Solid polycrystalline materials undergoing diffusion creep are usually described by Cauchy continuum models with a Newtonian viscous rheology dependent on the grain size. Such a continuum lacks the rotational degrees of freedom needed to describe grain rotation. Here we provide a more general continuum description of diffusion creep that includes grain rotation, and identifies the deformation of the material with that of a micropolar (Cosserat) fluid. We derive expressions for the micropolar constitutive tensors by a homogenisation of the physics describing a discrete collection of rigid grains, demanding an equivalent dissipation between the discrete and continuum descriptions. General constitutive laws are derived for both Coble (grain-boundary diffusion) and Nabarro-Herring (volume diffusion) creep. Detailed calculations are performed for a two-dimensional tiling of irregular hexagonal grains, which illustrates a potential coupling between the rotational and translational degrees of freedom. If only the plating out or removal of material at grain boundaries is considered, the constitutive laws are degenerate: modes of deformation that involve pure tangential motion at the grain boundaries are not resisted. This degeneracy can be removed by including the resistance to grain-boundary sliding, or by imposing additional constraints on the deformation.

New concepts are introduced to model strongly nonlinear resistive and reactive nonlinear power components. The models introduced are composed of linear time-invariant passive RLC elements, dependent sources, ideal switches, as well as constant voltage and current sources. In addition to the conventional component behavioural equations, these models are made complete by defining the so-called “control inequalities” between the terminal variables. Completely different components may lead to the same circuit model, but having different control inequalities, they perform their own characteristics. The method of component modelling is very convenient for the state–space analysis technique, the unification of which results in the complete state–-space description of the whole system. Even if there are discontinuities in the state variables, the analysis is possible without dealing with the theory of distributions, the problems of large and small time constants, and any numerical integration.