New Set Of Boundary Conditions Research Articles

A black hole toy model with non-local and boundary modes from non-trivial boundary conditions

We study gauge theories between two parallel boundaries with non-trivial boundary conditions, which serve as a toy model for black hole background with two boundaries near the horizon and infinite, aiming for a better understanding of the Bekenstein–Hawking entropy. The new set of boundary conditions allows boundary modes and non-local modes that interplay between the two boundaries. Those boundary modes and Wilson lines stretched between the two boundaries are carefully analyzed and are confirmed as physical variables in the phase space. Along with bulk fluctuation modes and topological modes, the partition function and entropy of all physical modes are evaluated via Euclidean path integral. It is shown that there are transitions between the dominance of different modes as we vary the temperature. The boundary fluctuation modes whose entropy is proportional to the volume dominate at high temperatures, and the boundary-area scaled boundary modes and Wilson lines are the more important at low temperatures. At super-low temperatures, when all the fluctuation modes die off, we see the topological modes whose entropy is the logarithm of the length scales of the system. The boundary modes and non-local modes should have their counterparts in a black hole system with similar boundary conditions, which might provide important hints for black hole physics.

Boundary conditions for molecular simulations of isolated elastic defects. Case study: The ⟨111⟩ screw dislocation in bcc W

A new set of boundary conditions is proposed for molecular simulations of isolated elastic defects such as dislocations and cracks. The case study of the ⟨111⟩ screw dislocation in body centered cubic (bcc) tungsten, modeled via a phenomenological, n-body cohesion functional, serves validating the new boundary conditions by computing structural properties of this defect and comparing these with results from the literature. Lowest energy configurations of the dislocated crystal have been obtained by molecular statics incorporating the new boundary conditions. The associated displacement and energy landscapes reveal conformal to the predictions of the elastic theory for a screw dislocation embedded in an infinitely extended crystal. In particular, no energy gradients and positional mismatch of atoms are found at the terminations of the computational box, validating thereby the new boundary conditions. Furthermore, it is shown that the structure, the spatial extension, and the excess energy of the two possible core polarizations of this dislocation compare consistently with existing findings for this and other bcc metals. Close to the dislocation line, energy minimization triggers the emergence of anelastic edge displacements extending over distances unexpectedly much larger than the dislocation core radius. Therefore, the conclusion is reached that in molecular simulations, the transverse to the dislocation line dimensions of the atomistic model should be taken considerably larger than it is accustomed. Perspectives opened by the present work are briefly discussed.

Boundary conditions for warped AdS3 in quadratic ensemble

In the context of warped conformal field theories (WCFT), the derivation of the warped Cardy formula relies on the zero mode spectrum being bounded from below. Generically, this is not true for holographic WCFTs in “canonical” ensemble, whereas this condition is satisfied in the “quadratic” ensemble, making it more natural in holographic setups. In this work, we find a new set of boundary conditions in three-dimensional Topologically Massive Gravity (TMG) such that the putative dual theory is a WCFT in quadratic ensemble. Surprisingly, imposing the equations of motion, we obtain a closed form metric spanned by two arbitrary chiral functions, analogous to the Bañados metrics in Einstein gravity. Surface charges for these boundary conditions are not a priori integrable and we discuss two choices of boundary conditions to make them so. We obtain the bulk thermodynamic entropy of warped BTZ black holes by making use of the warped Cardy formula, in its regime of validity. We also discuss the issue of identifying the vacuum in our solution space: demanding the enhancement of global symmetries selects only a family of solutions, out of which the unique vacuum must be carefully singled out.

Linear programming feedrate optimization

This paper focuses on two aspects of feedrate optimization via linear programming methods. Namely, the effect of curve sampling on time optimality of the resultant feedrate profile and a method of feedrate profile adaptation in response to a feedrate override command. A comparison of three distinct curve sampling approaches (uniform in parameter, uniform in arc length and curvature adaptive) is performed on a series of standard tool path curves. Results show that the curvature-adaptive sampling approach leads to substantial machining time reduction for tool path curves displaying high degree of curvature variation. Secondly, a method by which a new feedrate profile can be calculated in response to a feedrate override command is developed. The method formulates a new set of boundary conditions on the control point sequence of the feedrate curve in such a way that the resulting profile is guaranteed to coincide with the currently active profile up to the moment of override command, while minimizing the arc length necessary for transition to the newly commanded feedrate.

The generalized periodic boundary condition for microscopic simulations of heat transfer in heterogeneous materials

Porous and composite materials have been increasingly used in many heat transfer applications due to their enhanced thermal performance, and extensive studies have been conducted for a better scientific understanding of the heat transfer processes in such materials especially at the microscopic level. For heterogeneous materials with periodic microscopic structures, analysis can be performed over one such periodic unit if appropriate boundary conditions are applied. However, assumptions with no mathematical or physical justifications are often involved in previous studies, and this casts doubt on the accuracy and reliability of these results. In this study, a new set of boundary conditions are established based on rigorous mathematical derivations. The classical periodic boundary condition is generalized to incorporate the temperature differences between each pair of opposite boundaries of the periodic unit, and the global thermal gradient can be applied in arbitrary directions relative the structural periodicity. Also the interface between constituents in composite materials (or the fluid-solid interface in porous materials) is modeled according to the conjugate condition. This explicit approach incorporates the thermophysical properties of individual constituent materials and the possible thermal resistance at constituent interface, and thus provides a more complete and realistic representation of the heterogeneous system. This method with the generalized periodic boundary condition (GPBC) is carefully validated by comparing the temperature fields and effective conductivity for a two-dimensional (2D) heterogeneous model obtained from a direct simulation of a large domain size without using our boundary method and from one-unit simulations but with various periodic unit selections. The excellent agreement observed in these results indicates that our GPBC method correctly and accurately represents the underlying relationships in the thermal fields among periodic units. We also compare the simulation results for a 2D heterogeneous model with inclined poor conductivity rods in the middle, using our GPBC method and the insulated unit method (IUM) in previous publications; and remarkable differences in temperature fields and heat flux patterns are observed. Analysis and discussions are provided to show the unrealistic features in the IUM results due to the artificial assumptions on the boundary conditions. On the other hand, the temperature field from our GPBC method is consistent with intuitive physical considerations. The effects of constituent composition, conductivity and interface conductance on the effective thermal conductivity for a simple 2D heterogeneous material model, as well as the thermal flows with different Reynolds and Prandtl numbers through a staggered array of square blocks, are also examined. Despite the model simplicity, several interesting features are noticed, such as the heat flux response to changes in constituent conductivity and interface resistance and the saturation states of effective conductivity. Such information is valuable for a better understanding of the complex relationships between the microscopic structure and properties and the macroscopic thermal performances of composite and porous materials. The GPBC method developed in this work can also be readily implemented in typical numerical techniques in computational heat transfer such as the finite volume method, finite element method, and lattice Boltzmann method.

Superconformal Bondi-Metzner-Sachs Algebra in Three Dimensions.

The conformal extension of the BMS_{3} algebra is constructed. Apart from an infinite number of "superdilatations," in order to incorporate superspecial conformal transformations, the commutator of the latter with supertranslations strictly requires the presence of nonlinear terms in the remaining generators. The algebra appears to be very rigid, in the sense that its central extensions as well as the coefficients of the nonlinear terms become determined by the central charge of the Virasoro subalgebra. The wedge algebra corresponds to the conformal group in three spacetime dimensions SO(3,2), so that the full algebra can also be interpreted as an infinite-dimensional nonlinear extension of the AdS_{4} algebra with nontrivial central charges. Moreover, since the Lorentz subalgebra [sl(2,R)] is nonprincipally embedded within the conformal (wedge) algebra, according to the conformal weight of the generators, the conformal extension of BMS_{3} can be further regarded as a W_{(2,2,2,1)} algebra. An explicit canonical realization of the conformal extension of BMS_{3} is then shown to emerge from the asymptotic structure of conformal gravity in three dimensions, endowed with a new set of boundary conditions. The supersymmetric extension is also briefly addressed.

Integrable systems and the boundary dynamics of higher spin gravity on AdS3

We introduce a new set of boundary conditions for three-dimensional higher spin gravity with gauge group SL(3, ℝ) × SL(3, ℝ), where its dynamics at the boundary is described by the members of the modified Boussinesq integrable hierarchy. In the asymptotic region the gauge fields are written in the diagonal gauge, where the excitations go along the generators of the Cartan subalgebra of sl(3, ℝ) ⊕ sl(3, ℝ). We show that the entire integrable structure of the modified Boussinesq hierarchy, i.e., the phase space, the Poisson brackets and the infinite number of commuting conserved charges, are obtained from the asymptotic structure of the higher spin theory. Furthermore, its known relation with the Boussinesq hierarchy is inherited from our analysis once the asymptotic conditions are re-expressed in the highest weight gauge. Hence, the Miura map is recovered from a purely geometric construction in the bulk. Black holes that fit within our boundary conditions, the Hamiltonian reduction at the boundary, and the generalization to higher spin gravity with gauge group SL(N, ℝ) × SL(N, ℝ) are also discussed.

A new class of solutions of a generalized O(3)-sigma Chern-Simons model

In this work, we investigated the existence of compacton-like configuration in the O(3)-sigma model. We consider a minimally coupled O(3)-sigma model with a gauge field governed by a generalized Chern-Simons (CS) term. Contrary to that established in the literature, we impose a new set of boundary conditions and we find solutions to the variable fields and the respective energy density in the Bogomol'nyi limit. On the other hand, the introduction of a parameter ω in the Chern-Simons term can be adjusted to lead to finite-energy solutions of the model. Moreover, compact-like structures were studied with the evolution of this ω-generalized Chern-Simons term.

The influence of a lipid reservoir on the tear film formation.

We present a mathematical model to study the influence of a lipid reservoir, seen experimentally, at the lid margin on the formation and relaxation of the tear film during a partial blink. Applying the lubrication limit, we derive two coupled non-linear partial differential equations characterizing the evolution of the aqueous tear fluid and the covering insoluble lipid concentration. Departing from prior works, we explore a new set of boundary conditions (BCs) enforcing hypothesized lipid concentration dynamics at the lid margins. Using both numerical and analytical approaches, we find that the lipid-focused BCs strongly impact tear film formation and thinning rates. Specifically, during the upstroke of the eyelid, we find specifying the lipid concentration at the lid margin accelerates thinning. Parameter regimes that cause tear film formation success or failure are identified. More importantly, this work expands our understanding of the consequences of lipid dynamics near the lid margins for tear film formation.

Computation of the Lyapunov matrix for periodic time-delay systems and its application to robust stability analysis

A new procedure for computing the delay Lyapunov matrix for periodic time-delay systems that is based on the numerical solution of a partial differential equations (PDE) system is presented. The introduction of a new set of boundary conditions that are satisfied by the PDE system allows us to propose a new methodology for computing the initial conditions required by the implemented numerical scheme. The potential of the presented results is demonstrated by obtaining robust stability conditions depending on the delay Lyapunov matrix with respect to the system parameters, the delay and the frequency. The theoretical results are applied to the widely known delayed Mathieu equation.

Quasiclassical theory for interfaces with spin-orbit coupling

In recent years, substantial progress has been made regarding the application of quasiclassical theory on superconducting hybrid structures. This theoretical framework is reliant on a proper set of boundary conditions in order to describe multilayered systems. With the advent of the field of superconducting spintronics, systems which combine heavy metal layers, in which there is large spin--orbit coupling, with ferromagnets have received a great deal of attention, due to their potential for generating long range triplet superconductivity. In contrast to interfaces of strongly spin polarized materials, which are well understood, a quasiclassical theory for interfaces in systems where there is significant spin--orbit coupling does not yet exist. After reviewing the quasiclassical theory for interfaces, we here solve this problem by deriving a new set of boundary conditions which take spin--orbit coupling explicitly into account. We then go on to apply these boundary conditions to a superconductor-ferromagnet (SF) bilayer and an SFS Josephson weak link, demonstrating the emergence of long range triplet superconductivity in these systems.

Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies

We present a new set of boundary conditions for General Relativity on AdS3, where the dynamics of the boundary degrees of freedom are described by two independent left and right members of the Gardner hierarchy of integrable equations, also known as the “mixed KdV-mKdV” hierarchy. This integrable system has the very special property that simultaneously combines both, the Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) hierarchies in a single integrable structure. This relationship between gravitation in three-dimensional spacetimes and two-dimensional integrable systems is based on an extension of the recently introduced “soft hairy boundary conditions” on AdS3, where the chemical potentials are now allowed to depend locally on the dynamical fields and their spatial derivatives. The complete integrable structure of the Gardner system, i.e., the phase space, the Poisson brackets and the infinite number of commuting conserved charges, are directly obtained from the asymptotic analysis and the conserved surface integrals in the gravitational theory. These boundary conditions have the particular property that they can also be interpreted as being defined in the near horizon region of spacetimes with event horizons. Black hole solutions are then naturally accommodated within our boundary conditions, and are described by static configurations associated to the corresponding member of the Gardner hierarchy. The thermodynamic properties of the black holes in the ensembles defined by our boundary conditions are also discussed. Finally, we show that our results can be naturally extended to the case of a vanishing cosmological constant, and the integrable system turns out to be precisely the same as in the case of AdS3.

Three-dimensional numerical modelling of the drained/undrained transition for frequency-dependent elastic moduli and attenuation

SUMMARY In fully fluid-saturated rocks, two common phenomena are documented both experimentally and theoretically for frequency-dependent elastic moduli and attenuation, that is, the drained/undrained transition and the relaxed/unrelaxed transition. When investigating these transitions with the forced oscillation method in the laboratory, it is crucial to consider the boundary differences between the laboratory and the underground. A 1-D poroelastic numerical model was previously established to describe these differences and their effects; however, the boundary conditions used in the model are actually different from the real experiment case, thus leading to inaccurate predication of the measurement results in a laboratory. In this paper, we established a 3-D poroelastic numerical model with a new set of boundary conditions that better represent the experiment conditions. Furthermore, the 3-D poroelastic modelling results were compared with laboratory measurements under the same boundary conditions, showing a much better fit than the 1-D model. Therefore, the 3-D model provides a more accurate and reliable approach to understand the regimes and transitions of elastic modulus dispersion and attenuation, and thus has great importance in interpreting the measurements of frequency-dependent properties of rocks in the laboratory.

New inflow boundary conditions for modeling twisted wind profiles in CFD simulation for evaluating the pedestrian-level wind field near an isolated building

The hilly topography of Hong Kong influences oncoming winds and gradually changes their wind directions along the profiles' height. The vertical variation in wind directions, or the twist effect, significantly influences the Pedestrian Level Wind (PLW) field in urban areas of Hong Kong, thus it is a topic demanding systematic investigations. In this study, a new set of inflow boundary conditions are proposed to model twisted wind flows in Computational Fluid Dynamic (CFD) simulations. The new inflow boundary condition derived based on the horizontal homogeneous assumption, specifies a vertical profile of lateral wind speeds at the inlet boundary to sustain the twist effect in the empty computational domain. The proposed boundary conditions are used to simulate the PLW fields near three isolated buildings with different Height-to-Width ratio using two CFD codes; OpenFOAM, and FLUENT. The results reveal that OpenFOAM is more reliable in simulating PLW fields in twisted wind flows using the new set of boundary conditions. The three-dimensional flow field provided by the OpenFOAM simulation shows sparse streamlines downstream the buildings, indicating lack of organized eddies in the building far wake, which negatively affects the dispersion of air pollutants in twisted winds.

Higher spin black holes with soft hair

We construct a new set of boundary conditions for higher spin gravity, inspired by a recent "soft Heisenberg hair"-proposal for General Relativity on three-dimensional Anti-de Sitter. The asymptotic symmetry algebra consists of a set of affine $\hat u(1)$ current algebras. Its associated canonical charges generate higher spin soft hair. We focus first on the spin-3 case and then extend some of our main results to spin-$N$, many of which resemble the spin-2 results: the generators of the asymptotic $W_3$ algebra naturally emerge from composite operators of the $\hat u(1)$ charges through a twisted Sugawara construction; our boundary conditions ensure regularity of the Euclidean solutions space independently of the values of the charges; solutions, which we call "higher spin black flowers", are stationary but not necessarily spherically symmetric. Finally, we derive the entropy of higher spin black flowers, and find that for the branch that is continuously connected to the BTZ black hole, it depends only on the affine purely gravitational zero modes. Using our map to $W$-algebra currents we recover well-known expressions for higher spin entropy. We also address higher spin black flowers in the metric formalism and achieve full consistency with previous results.

Boundary conditions at the ablative walls in two-temperature modelling of thermal plasmas with reactive working gas

In this paper, we propose a new set of boundary conditions at ablative hot walls with thermionic electron emission for two-temperature thermal arc models in which the temperature of electrons can deviate from the temperature of heavy particles,. The boundary conditions are for the electric potential, the two energy equations for electrons and heavy particles (ions and neutrals), and the two mass conservation equations for the working gas and the vapour of the wall material. In these boundary conditions, the plasma sheath formed at the wall is viewed as the interface between the plasma and the wall, the plasma composition is assumed to be determined by a generalized Saha equation adapted to the case , and the reactive gas is assumed to form a stoichiometric film at the wall. The derived boundary conditions allow the calculation of the heat flux from the plasma to the wall, the thermionic electron current density, and the erosion rate of the wall that makes the model of wall–plasma interaction self-consistent. The derived boundary conditions are reduced to the case of non-reactive working gas and to the case of walls with materials with a low melting point, such as copper, where the thermionic electron emission of the wall is small and can be neglected. The case of the boundary conditions for high-pressure arcs burning in the vapour of the wall material (no working gas) is also considered. The boundary conditions obtained are applied to the cathode spot at an ablative tungsten cathode and to the anode attachment at a copper anode in argon.

Null warped AdS in higher spin gravity

We equip three-dimensional spin-3 gravity in the principal embedding with a new set of boundary conditions that we call "asymptotically null warped AdS". We find a chiral copy of the Polyakov-Bershadsky algebra as asymptotic symmetry algebra, reminiscent of the situation in topologically massive gravity with strict null warped AdS boundary conditions. We prove the invertibility of the map between zuvielbein and metric variables and construct a global gauge transformation to half of AdS spin-3 gravity in the diagonal embedding. This explains why the theory is chiral and why the Polyakov-Bershadsky algebra arises. We then introduce chemical potentials, derive the entropy, free energy, and the holographic response functions, and conclude with a discussion.

Plane elasticity solutions for beams with fixed ends

The plane stress problem of beams is a typical one in elasticity theory. In this paper a new set of boundary conditions for the fixed end is proposed to improve the accuracy of the plane elasticity solution for beams with fixed end(s). Plane elasticity solutions are then derived for the cantilever beam, propped cantilever beam, and fixed-fixed beam. The new set of boundary conditions is constructed by combining two conventional ones with a parameter. The parameters for different kinds of beams are determined by minimizing the square sum of the longitudinal displacements through the thickness of the fixed end. Comparison with the results obtained by the finite element method (FEM) shows the efficiency of the new type of boundary conditions. When the beam is a deep one, it is found that different boundary conditions yield different errors, and the elasticity solution obtained by the new boundary conditions best approaches the FEM results.

A novel computational model for the hemodynamics of bileaflet mechanical valves in the opening phase.

A powerful alternative means to study the hemodynamics of bileaflet mechanical heart valves is the computational fluid dynamics method. It is well recognized that computational fluid dynamics allows reliable physiological blood flow simulation and measurements of flow parameters. To date, in almost all of the modeling studies on the hemodynamics of bileaflet mechanical heart valves, a velocity (mass flow)-based boundary condition and an axisymmetric geometry for the aortic root have been assigned, which, to some extent, are erroneous. Also, there have been contradictory reports of the profile of velocity in downstream of leaflets, that is, in some studies, it is suggested that the maximum blood velocity occurs in the lateral orifice, and in some other studies, it is postulated that the maximum velocities in the main and lateral orifices are identical. The reported values for the peak velocities range from 1 to 3 m/s, which highly depend on the model assumptions. The objective of this study is to demonstrate the importance of the exact anatomical model of the aortic root and the realistic boundary conditions in the hemodynamics of the bileaflet mechanical heart valves. The model considered in this study is based on the St Jude Medical valve in a novel modeling platform. Through a more realistic geometrical model for the aortic root and the St Jude Medical valve, we have developed a new set of boundary conditions in order to be used for the assessment of the hemodynamics of aortic bileaflet mechanical heart valves. The results of this study are significant for the design improvement of conventional bileaflet mechanical heart valves and for the design of the next generation of prosthetic valves.

Excision scheme for black holes in constrained evolution formulations: Spherically symmetric case

Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead appropriate boundary conditions at the excised surface. In this work we present recent developments of this technique in the case of constrained formulations of Einstein equations and for spherically symmetric spacetimes. We present a new set of boundary conditions to apply to the elliptic system in the fully-constrained formalism of Bonazzola et al. (2004), at an arbitrary coordinate sphere inside the apparent horizon. Analytical properties of this system of boundary conditions are studied and, under some assumptions, an exponential convergence toward the stationary solution is exhibited for the vacuum spacetime. This is verified in numerical examples, together with the applicability in the case of the accretion of a scalar field onto a Schwarzschild black hole. We also present the successful use of the excision technique in the collapse of a neutron star to a black hole, when excision is switched on during the simulation, after the formation of the apparent horizon. This allows the accretion of matter remaining outside the excision surface and for the stable long-term evolution of the newly formed black hole.