Presence Of Boundary Conditions Research Articles

On the analyticity of the pressure for a non-ideal gas with high density boundary conditions

We consider a continuous system of classical particles confined in a cubic box Λ interacting through a stable and finite range pair potential with an attractive tail. We study the Mayer series of the grand canonical pressure of the system pΛω(β,λ) at inverse temperature β and fugacity λ in the presence of boundary conditions ω belonging to a very large class of locally finite particle configurations. This class of allowed boundary conditions is the basis for any probability measure on the space of locally finite particle configurations satisfying the Ruelle estimates. We show that the pΛω(β,λ) can be written as the sum of two terms. The first term, which is analytic and bounded as the fugacity λ varies in a Λ-independent and ω-independent disk, coincides with the free-boundary-condition pressure in the thermodynamic limit. The second term, analytic in a ω-dependent convergence radius, goes to zero in the thermodynamic limit. As far as we know, this is the first rigorous analysis of the behavior of the Mayer series of a non-ideal gas subjected to non-free and non-periodic boundary conditions in the low-density/high-temperature regime when particles interact through a non-purely repulsive pair potential.

Fourier series and Search Space Reduction based Control profiles for Reentry Trajectory Optimization

In this paper, the reentry trajectory of a space shuttle is obtained using search space reduction (SSR) optimization technique along with the finite Fourier series-based parametrization of control variables. The reentry trajectory design for the space shuttle is most important and challenging because of non-linear entry dynamics, the vehicle being unpowered, the presence of boundary conditions and path constraints that are to be satisfied accurately. To solve this problem, it is essential to find optimal control profiles such as bank angle and angle of attack using which optimal reentry trajectory is generated. In this paper, finite Fourier series-based parametrization of the angle of attack and bank angle is proposed. To show that this novel parametrization approach results in a reentry trajectory, three reentry mission objectives are considered such as maximizing the crossrange, minimizing the total heat experienced by the vehicle and minimizing the total heat with mínimum oscillations in reentry trajectory. Further, the optimal Fourier coefficients are obtained using the search space reduction optimization technique to achieve mentioned reentry mission objectives. The simulation results show that this parametrization method has resulted in optimal reentry trajectories which satisfy the terminal constraints accurately.

A novel model of non-linear radiative Williamson nanofluid flow along a vertical wavy cone in the presence of gyrotactic microorganisms

ABSTRACT A novel mathematical technique for an unsteady bioconvective flow of Williamson nanofluids over a vertical wavy cone in the presence of non-linear radiation and viscous dissipation impacts is investigated. The cone surface is described by a sinusoidal function while the components of the extra stress tensor are presented in terms of the dynamic viscosity. The irregular wavy surface is referred to the convective boundary conditions and nanoparticle passively controls conditions. The governing equations are presented in general forms then the condition and suitable transformations are used to map the wavy cone to regular domain. A fully implicit finite differences method (FDM) is applied to solve the converted system and wide ranges of independent variables are assumed. . The major outcomes disclosed that the increase in the Williamson number causes a reduction the nanofluid flow while the skin friction coefficient is rising. Further, there is an enhancement in the values of the Nusselt number up to 75% is obtained as Biot number is altered from 0.1 to 0.4. Also, the convective boundary conditions in presence of the non-linear radiations are recommended to enhance the velocity, temperature and rate of the heat transfer.

Electromagnetic scattering by a partially graphene-coated dielectric cylinder: Efficient computation and multiple plasmonic resonances.

We present a numerical approach for the solution of electromagnetic scattering from a dielectric cylinder partially covered with graphene. It is based on a classical Fourier-Bessel expansion of the fields inside and outside the cylinder to which we apply ad hoc boundary conditions in the presence of graphene. Due to the singular nature of the electric field at the edges of the graphene sheet, we introduce auxiliary boundary conditions. The result is a particularly simple and efficient method allowing the study of diffraction from such structures. We also highlight the presence of multiple plasmonic resonances that we ascribe to the surface modes of the coated cylinder.

MHD Non-Aligned Stagnation-Point Flow of Nanofluid over a Stretching Surface with a Convective Boundary Condition

In the present paper, MHD non-aligned stagnation-point flow has been found to be interesting and innovative in the analysis of viscous nanofluids over a stretching surface with a convective boundary condition in presence of the porous medium. Due to its many engineering and industrial uses, such as cooling nuclear reactors during an emergency shutdown, soft sheet extrusion, metal spinning, and solar central receivers exposed to wind current, the study of oblique stagnation point flow is important. The suitable similarity transformation is utilized for the reduction of a set of governing equations, which are solved by using the Differential Transformation Method (DTM) with Maple software. The Nusselt number (Nux), skin friction (Cf), and Sherwood number (Shx) are tabulated. A strong agreement is seen, and the accuracy of the results tabulated using DTM and the numerical method (fourth-order Runge-Kutta-Fehlberg integration scheme) is illustrated. Further, velocity, temperature, and nanoparticle volume fraction profiles are shown graphically and studied various parameters. It is reported that the magnetic parameter reduces the axial and oblique velocity gradients while enhancing the temperature and volume fraction profiles. The porosity parameter reduces the axial and oblique velocity gradients while enhancing the temperature profile.

Structural identifiability analysis of age-structured PDE epidemic models.

Computational and mathematical models rely heavily on estimated parameter values for model development. Identifiability analysis determines how well the parameters of a model can be estimated from experimental data. Identifiability analysis is crucial for interpreting and determining confidence in model parameter values and to provide biologically relevant predictions. Structural identifiability analysis, in which one assumes data to be noiseless and arbitrarily fine-grained, has been extensively studied in the context of ordinary differential equation (ODE) models, but has not yet been widely explored for age-structured partial differential equation (PDE) models. These models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. In this work, we establish a pipeline for structural identifiability analysis of age-structured PDE models using a differential algebra framework and derive identifiability results for specific age-structured models. We use epidemic models to demonstrate this framework because of their wide-spread use in many different diseases and for the corresponding parallel work previously done for ODEs. In our application of the identifiability analysis pipeline, we focus on a Susceptible-Exposed-Infected model for which we compare identifiability results for a PDE and corresponding ODE system and explore effects of age-dependent parameters on identifiability. We also show how practical identifiability analysis can be applied in this example.

Effective Hamiltonians in Nonrelativistic Quantum Electrodynamics

In this paper, we consider some second-order effective Hamiltonians describing the interaction of the quantum electromagnetic field with atoms or molecules in the nonrelativistic limit. Our procedure is valid only for off-energy-shell processes, specifically virtual processes such as those relevant for ground-state energy shifts and dispersion van der Waals and Casimir-Polder interactions, while on-energy-shell processes are excluded. These effective Hamiltonians allow for a considerable simplification of the calculation of radiative energy shifts, dispersion, and Casimir-Polder interactions, including in the presence of boundary conditions. They can also provide clear physical insights into the processes involved. We clarify that the form of the effective Hamiltonian depends on the field states considered, and consequently different expressions can be obtained, each of them with a well-defined range of validity and possible applications. We also apply our results to some specific cases, mainly the Lamb shift, the Casimir-Polder atom-surface interaction, and the dispersion interactions between atoms, molecules, or, in general, polarizable bodies.

SOUND PROPAGATION THROUGH STRUCTURAL COMPONENTS UNDER CONDITIONS OF NON-RIGID CONTACT AT THE BOUNDARIES BETWEEN THEM

The report considers the problem statement, derivation and solution of the dispersion equation for sound propagation in a layered inhomogeneous medium with oriented fracturing, simulated by the presence of boundary conditions in the "linear slip" approximation. Numerical solutions are obtained and analyzed for the frequency range and values of the parameters of contact breaking, which is relevant in the problems of ultrasonic measurements

Programmable mechanical metastructures from locally bistable domes

Mechanical metamaterials have introduced a paradigm shift in materials development by offering property control through geometrical design at the micro/mesoscale. The ensuing design flexibility has opened up avenues to leverage geometrical nonlinearities in the microstructure design to allow for realizing uncharacteristic global functionalities beyond the scope of traditional materials. In this work, we report on a class of programmable stiffness metastructures designed by patterning locally bistable dome units in structural element geometries. The global response characteristics of our metastructures reversibly switch between a plate-like response and a shell-like response as the bistable domes are switched locally between their two stable states. This allows for up to an order of magnitude variation in the global stiffness. Furthermore, we demonstrate the ability of our metastructures to enable in-situ property programmability in the presence of boundary conditions, thus paving the way for successful integration into larger structures. Uniquely, our architecture allows for multi-directional linear and nonlinear response programmability, while operating under different loading environments. As such, the presented designs can potentially serve as blueprint models to realize a new class of load-carrying, robust, programmable systems for soft robotics and morphing aerospace structures.

Mixed Convection Flow Of Viscoelastic Nanofluid Past A Horizontal Circular Cylinder In Presence Of Heat Generation

The steady two-dimensional mixed convection boundary layer flow of viscoelastic nanofluid past a horizontal circular cylinder with convective boundary condition in presence of heat generation has been studied numerically. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and copper as a nanoparticle with the Prandtl number Pr = 6.2. The Tiwari and Das model has been considered in this study. The governing partial differential equations are reduced to a system of ordinary differential equations by introducing similarity transformations. The nonlinear similarity equations are solved numerically by applying the Keller-box method. The numerical results are presented graphically for different values of the parameters including the heat generation parameter, nanoparticles volume fraction, and Biot number. A systematic study is discussed to analyze the effect of these parameters on the velocity and temperature profiles as well as the skin friction and heat transfer coefficient. The thermal boundary layer shows the changes in variation behavior when the nanoparticles volume fraction, heat generation and Biot number are increased. Heat transfer coefficient is increasing function of heat generation parameter. Nanoparticles volume fraction on heat transfer coefficient have opposite effect when compared with heat generation parameter.

A WKB formula for echoes

We present a unified approach for the study of idealized gravitational compact objects like wormholes (WHs) and horizonless stars, here simulated by the presence of boundary conditions at a deeply inner wall. At the classical level, namely neglecting quantum effects, the presence of the wall leads to characteristic echoes following the usual ringdown phase, such that it can discriminate black holes from other horizonless, and probably exotic, compact objects. With regard to this issue, an analytical though approximated expression for the complex frequencies of the quasinormal echoes is found and discussed. At the quantum level, we show that static WHs do not radiate.

On the Stability of FDTD-Based Numerical Codes to Evaluate Lightning-Induced Overvoltages in Overhead Transmission Lines

One of the main issues that has to be faced when evaluating lightning-induced overvoltages on a realistic network configuration is to implement the algorithm that solves the field-to-line coupling problem into an electromagnetic simulator that is able to represent with a high level of detail all the power system components. On one hand, numerical stability conditions of the finite-difference time-domain schemes have been deeply investigated in the presence of boundary conditions known analytically; on the other hand, there is not so much literature on the situations in which such conditions are provided in a numerical way through an external electromagnetic simulator. The study reveals that the commonly used linear extrapolation of currents at the line extremities might rise to numerical instabilities. An efficient solution using the method of characteristics is presented and validated.

Dynamical Casimir effect in a double tunable superconducting circuit

We present an analytical and numerical analysis of the particle creation in a cavity ended with two SQUIDs, both subjected to time dependent magnetic fields. In the linear and lossless regime, the problem can be modeled by a free quantum field in $1+1$ dimensions, in the presence of boundary conditions that involve a time dependent linear combination of the field and its spatial and time derivatives. We consider a situation in which the boundary conditions at both ends are periodic functions of time, focusing on interesting features as the dependence of the rate of particle creation with the characteristics of the spectrum of the cavity, the conditions needed for parametric resonance, and interference phenomena due to simultaneous time dependence of the boundary conditions. We point out several concrete effects that could be tested experimentally

Boundary enhanced effects on the existence of quadratic solitons

We investigate, both analytically and numerically, the boundary enhanced effects exerted on the quadratic solitons consisting of fundamental waves and oscillatory second harmonics in the presence of boundary conditions. The nonlocal analogy predicts that the soliton for fundamental wave is supported by the balance between equivalent nonlinear confinement and diffraction (or dispersion). Under Snyder and Mitchell’s strongly nonlocal approximation, we obtain the analytical soliton solutions both with and without the boundary conditions to show the impact of boundary conditions. We can distinguish explicitly the nonlinear confinement between the second harmonic mutual interaction and the enhanced effects caused by remote boundaries. Those boundary enhanced effects on the existence of solitons can be positive or negative, which depend on both sample size and nonlocal parameter. The piecewise existence regime of solitons can be explained analytically. The analytical soliton solutions are verified by the numerical ones and the discrepancy between them is also discussed.

The Dynamics of Neural Fields on Bounded Domains: An Interface Approach for Dirichlet Boundary Conditions

Continuum neural field equations model the large-scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded as well as unbounded domains. Neural field models do not require the specification of boundary conditions. Relatively little attention has been paid to the imposition of neural activity on the boundary, or to its role in inducing patterned states. Here we redress this imbalance by studying neural field models of Amari type (posed on one- and two-dimensional bounded domains) with Dirichlet boundary conditions. The Amari model has a Heaviside nonlinearity that allows for a description of localised solutions of the neural field with an interface dynamics. We show how to generalise this reduced but exact description by deriving a normal velocity rule for an interface that encapsulates boundary effects. The linear stability analysis of localised states in the interface dynamics is used to understand how spatially extended patterns may develop in the absence and presence of boundary conditions. Theoretical results for pattern formation are shown to be in excellent agreement with simulations of the full neural field model. Furthermore, a numerical scheme for the interface dynamics is introduced and used to probe the way in which a Dirichlet boundary condition can limit the growth of labyrinthine structures.

Cu-water nanofluid flow induced by a vertical stretching sheet in presence of a magnetic field with convective heat transfer

The convective heat transfer performance of nanofluid over a permeable stretching sheet with thermal convective boundary condition in presence of magnetic field and slip velocity is studied in the present paper. Cu-water nanofluid is used to investigate the effect of nanoparticles on the flow and heat transfer characteristic. The numerical results are compared with published results and are found in an excellent agreement. The influences of various relevant parameters on the velocity and temperature as well as the rate of shear stress and the rate of heat transfer are elucidated through graphs and tables. It is observed that nanoparticles volume fraction and surface convection parameter both increase the thickness of thermal boundary layer.

Invasions Slow Down or Collapse in the Presence of Reactive Boundaries

Motivated by the propagation of thin bacterial films around planar obstacles, this paper considers the dynamics of travelling wave solutions to the Fisher–KPP equation u_t = u(1-u) + u_{xx} + u_{yy} in a planar strip -infty< x < infty , 0 le y le L. We examine the propagation of fronts in the presence of a mixed boundary condition (also referred to as a ‘partially absorbing’ or ‘reactive’ boundary) u_y = alpha u, with alpha >0, at y=0. The presence of boundary conditions of this kind leads to the development of front solutions that propagate in x but contain transverse structure in y. Motivated by the observation that the speed of propagation in the Fisher–KPP equation is determined (for exponentially decaying initial conditions) by the behaviour at the leading edge, we analyse the linearised Fisher–KPP equation in order to estimate the speed of the stable travelling front, a function of the width L and the imposed boundary conditions. For wide strips the speed estimate based on the linearised equation agrees well with the results of numerical simulations. For narrow channels numerical simulations indicate that the stable front propagates more slowly, and for sufficiently small L or sufficiently large alpha the front speed falls to zero and the front collapses. The reason for the collapse is the non-existence, far behind the front, of a stable positive equilibrium solution u(x, y). While existence of these equilibrium states can be demonstrated via phase plane arguments, the investigation of stability is similar to calculations of critical patch sizes carried out in similar ecological models.

Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy

In this paper, we investigated the thermal behavior in living biological tissues using time fractional dual-phase-lag bioheat transfer (DPLBHT) model subjected to Dirichelt boundary condition in presence of metabolic and electromagnetic heat sources during thermal therapy. We solved this bioheat transfer model using finite element Legendre wavelet Galerkin method (FELWGM) with help of block pulse function in sense of Caputo fractional order derivative. We compared the obtained results from FELWGM and exact method in a specific case, and found a high accuracy. Results are interpreted in the form of standard and anomalous cases for taking different order of time fractional DPLBHT model. The time to achieve hyperthermia position is discussed in both cases as standard and time fractional order derivative. The success of thermal therapy in the treatment of metastatic cancerous cell depends on time fractional order derivative to precise prediction and control of temperature. The effect of variability of parameters such as time fractional derivative, lagging times, blood perfusion coefficient, metabolic heat source and transmitted power on dimensionless temperature distribution in skin tissue is discussed in detail. The physiological parameters has been estimated, corresponding to the value of fractional order derivative for hyperthermia treatment therapy.

Infrared computations of defect Schur indices

We conjecture a formula for the Schur index of N=2 four-dimensional theories in the presence of boundary conditions and/or line defects, in terms of the low-energy effective Seiberg-Witten description of the system together with massive BPS excitations. We test our proposal in a variety of examples for SU(2) gauge theories, either conformal or asymptotically free. We use the conjecture to compute these defect-enriched Schur indices for theories which lack a Lagrangian description, such as Argyres-Douglas theories. We demonstrate in various examples that line defect indices can be expressed as sums of characters of the associated two-dimensional chiral algebra and that for Argyres-Douglas theories the line defect OPE reduces in the index to the Verlinde algebra.

Homotopy Analysis Solution to Thermal Radiation Effects on MHD Boundary Layer Flow and Heat Transfer Towards an Inclined Plate with Convective Boundary Conditions

This paper investigates the Magnetohydrodynamic flow and heat transfer towards a stationary/moving plate with convective boundary conditions in presence of thermal radiation. The governing equations are simplified by similarity transformations which are then solved by homotopy analysis method (HAM). Effects of emerging parameters such as Prandtl number, local Grashof number, Magnetic parameter, Radiation parameter and the Biot number on the velocity field and temperature field are plotted and discussed. It is found that the temperature of the stationary flat plate is higher than the temperature of the moving flat plate. The obtained results are compared with other results obtain in previous works so that the high accuracy of the present result is apparent.