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This study investigates the impact of structural configurations, boundary conditions, and atomic number on the Curie transition temperature ($T_c)$ of bulk cobalt (Co) utilizing Monte Carlo simulations. The analysis reveals that the Curie temperature increases as the structure transitions from a simple cubic (SC) to a body-centered cubic (BCC), hexagonal close-packed (HCP), and face-centered cubic (FCC) configuration. The SC structure, exhibiting the lowest $T_c$, serves as the reference for evaluating these influencing factors. The study also demonstrates that nonperiodic boundary conditions yield the lowest $T_c$ compared to periodic ones. Additionally, an increase in the number of atoms from 4000 to 108,000 under nonperiodic boundary conditions correlates with an increase in $T_c$. These findings are consistent with experimental data and provide a foundational basis for researchers involved in the synthesis and application of bulk Co in devices, biomedical applications at room temperature, and emerging technologies.

Conformal quantum field theory on the half-space x>0 of Minkowski space-time ("boundary CFT") is analyzed from an algebraic point of view, clarifying in particular the algebraic structure of local algebras and the bi-localized charge structure of local fields. The field content and the admissible boundary conditions are characterized in terms of a non-local chiral field algebra.

In the framework of the functional renormalization group and of the perturbative, algebraic approach to quantum field theory (pAQFT), in D’Angelo et al. [Ann. Henri Poinc.25 (2024) 2295–2352] it has been derived a Lorentzian version of a flow equation à la Wetterich, which can be used to study nonlinear, quantum scalar field theories on a globally hyperbolic spacetime. In this work, we show that the realm of validity of this result can be extended to study interacting scalar field theories on globally hyperbolic manifolds with a timelike boundary. By considering the specific examples of half-Minkowski spacetime and of the Poincaré patch of Anti-de Sitter, we show that the form of the Lorentzian Wetterich equation is strongly dependent on the boundary conditions assigned to the underlying field theory. In addition, using a numerical approach, we are able to provide strong evidences that there is a qualitative and not only a quantitative difference in the associated flow and we highlight this feature by considering Dirichlet and Neumann boundary conditions on half-Minkowski spacetime.

In the study of QCD dynamics, C^⋆ boundary conditions are physically relevant in certain cases. In this paper, we study the implementation of these boundary conditions in the lattice formulation of full QCD with staggered fermions. In particular, we show that the usual even-odd partition trick to avoid the redoubling of the fermion matrix is still valid in this case. We give an explicit implementation of these boundary conditions for the Hybrid Monte Carlo algorithm.

Interfaces between coexisting phases are very common in condensed matter physics, and thus many simulations attempt to characterize their properties, in particular, the interfacial tension and the interfacial profile. However, while theory usually deals with the "intrinsic profile", the latter is not a straightforward output of a simulation: The actual profile (observed in simulations and/or experiments!) is broadened by lateral fluctuations. Therefore, in the usual simulation geometry of L × L × L (in three dimensions), where one chooses suitable boundary conditions to stabilize one or two interfaces of (minimal) area L × L, the profile (and in particular the interfacial width) depends on both linear dimensions L and D (parallel and perpendicular to the interface). Choosing recent simulations of interfaces between coexisting phases of unmixed binary polymer mixtures as an example, we show that this interfacial broadening is not a small correction, but has pronounced effects; for a reliable data analysis, it is (unfortunately!) necessary to vary L and D over a wide range. We present counterexamples to the widespread belief that for small linear dimensions, the intrinsic profile is straightforwardly recovered and speculate about conditions where this belief may be valid.

A new boundary condition is developed to enhance numerical stability for moving walls in lattice-Boltzmann simulations. It includes a population "adjustment" procedure at boundaries which allows stable simulations closer to the theoretical limit of τ = 0.5. Couette and lid-driven cavity flow simulations show improved velocity profiles, lower stable relaxation timestep τ and higher Reynolds number Re limits. The new method needs fewer timesteps to achieve steady-state.

Nonparticulate continuum descriptions allow for computationally efficient modeling of suspension flows at scales that are inaccessible to more detailed particulate approaches. It is well known that the presence of particles influences the effective viscosity of a suspension and that this effect has thus to be accounted for in macroscopic continuum models. The present paper aims at developing a nonparticulate model that reproduces not only the rheology but also the cell-induced velocity fluctuations, responsible for enhanced diffusivity. The results are obtained from a coarse-grained blood model based on the lattice Boltzmann (LB) method. The benchmark system comprises a flow between two parallel plates with one of them featuring a smooth obstacle imitating a stenosis. Appropriate boundary conditions are developed for the particulate model to generate equilibrated cell configurations mimicking an infinite channel in front of the stenosis. The averaged flow field in the bulk of the channel can be described well by a nonparticulate simulation with a matched viscosity. We show that our proposed phenomenological model is capable to reproduce many features of the velocity fluctuations.

In this paper, we present a simulator for two-particle quantum walks on the line and one-particle on a two-dimensional squared lattice. It can be used to investigate the equivalence between the two cases (one- and two-particle walks) for various boundary conditions (open, circular, reflecting, absorbing and their combinations). For the case of a single walker on a two-dimensional lattice, the simulator can also implement the Möbius strip. Furthermore, other topologies for the walker are also simulated by the proposed tool, like certain types of planar graphs with degree up to 4, by considering missing links over the lattice. The main purpose of the simulator is to study the genuinely quantum effects on the global properties of the two-particle joint probability distribution on the entanglement between the walkers/axis. For that purpose, the simulator is designed to compute various quantities such as: the entanglement and classical correlations, (classical and quantum) mutual information, the average distance between the two walkers, different hitting times and quantum discord. These quantities are of vital importance in designing possible algorithmic applications of quantum walks, namely in search, 3-SAT problems, etc. The simulator can also implement the static partial measurements of particle(s) positions and dynamic breaking of the links between certain nodes, both of which can be used to investigate the effects of decoherence on the walker(s). Finally, the simulator can be used to investigate the dynamic Anderson-like particle localization by varying the coin operators of certain nodes on the line/lattice. We also present some illustrative and relevant examples of one- and two-particle quantum walks in various scenarios. The tool was implemented in C and is available on-line at http://qwsim.weebly.com/.

This paper presents a systematic study on a basic kind of outflow boundary condition for Dissipative Particle Dynamics (DPD) simulation, in which the flow near the outlet can be assumed as fully developed. The boundary conditions are expressed in Neumann-type constraints due to the zero gradients of hydrodynamic quantities on the boundary. The flow rate is included as an additional constraint to ensure the stability of a simulation. The boundary conditions are imposed through a reservoir, which is a replica of the simulation domain in the vicinity of the outlet. All the particle configurations are conserved in the reservoir. A velocity adjusting scheme is developed for the reservoir in order to control the deviation of the outflow rate and to remove the pressure discontinuity across the boundary. The effectiveness of the boundary method is examined through the simulations of a uniform flow and a laminar flow in a bifurcated tunnel. The outflow rates, as well as the velocity profile and pressure distribution, all agree well with the Navier–Stokes solution by comparison. The assumption of the fully developed outflow is validated by measuring the gradients of the flow rates. It is expected that this boundary method can be used in the simulation of flows with heterogeneous particle distribution, without having to evaluate the distribution function in advance.

We propose a novel local boundary condition for three-dimensional Schrödinger equation under spherical coordinates. It is based on the approximate linear relationship among the Bessel functions from a free one-dimensional Schrödinger equation. With a variable transform, the novel boundary condition is a simple form of some ordinary differential equations, which relate the grid point near the numerical boundaries. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary conditions.

In recent years, physics-informed neural networks (PINNs) have come to the foreground in many disciplines as a new way to solve partial differential equations. Compared with traditional discrete methods and data-driven surrogate models, PINNs can learn the solutions of partial differential equations without relying on tedious mesh generation and simulation data. In this paper, an original neural network structure PINN-FFHT based on PINNs is devised to solve the fluid flow and heat transfer problems. PINN-FFHT can simultaneously predict the flow field and take into consideration the influence of flow on the temperature field to solve the energy equation. A flexible and friendly boundary condition (BC) enforcement method and a dynamic strategy that can adaptively balance the loss term of velocity and that of temperature are proposed for training PINN-FFHT, serving to accelerate the convergence and improve the accuracy of predicted results. Three cases are predicted to validate the capabilities of the network, including the laminar flow with the Dirichlet BCs in heat transfer, respectively, under the Cartesian and the cylindrical coordinate systems, and the thermally fully developed flow with the Neumann BCs in heat transfer. Results show that PINN-FFHT is faster in convergence speed and higher in accuracy than traditional PINN methods.

A Monte Carlo method with boundary conditions of a self-consistent maximum entropy type has been applied to the classical Heisenberg model.

An improved sparse-matrix factorization technique for the transfer matrix of the hard-square lattice gas is proposed to perform exact diagonalization up to the strip width N = 34. The critical point, critical free-energy density, and universal parameters are determined accurately. The eigenvalue spectrum of the transfer matrix is also precisely investigated at the critical point for different boundary conditions.

The accuracy of the lattice-Boltzmann method (LBM) is moderated by several factors, including Mach number, spatial resolution, boundary conditions, and the lattice mean free path. Results obtained with 3D lattices suggest that the accuracy of certain two-dimensional (2D) flows, such as Poiseuille and Couette flow, persist even when the mean free path between collisions is large, but that of the 3D duct flow deteriorates markedly when the mean free path exceeds the lattice spacing. Accuracy in general decreases with Knudsen number and Mach number, and the product of these two quantities is a useful index for the applicability of LBM to 3D low-Reynolds-number flow. The influence of boundary representations on LBM accuracy is captured by the proposed index, when the accuracy of the prescribed boundary conditions is consistent with that of LBM.

The lattice-Boltzmann (LB) method is applied to complex, moving geometries in which computational cells are partially filled with fluid. The LB algorithm is modified to include a term that depends on the percentage of the cell saturated with fluid. The method is useful for modeling suspended obstacles that do not conform to the grid. Another application is to simulations of flow through reconstructed media that are not easily segmented into solid and liquid regions. A detailed comparison is made with FIDAP simulation results for the flow about a periodic line of cylinders in a channel at a non-zero Reynolds number. Two cases are examined. In the first simulation, the cylinders are given a constant velocity along the axis of the channel, and the steady solution is acquired. The transient behavior of the system is then studied by giving the cylinders an oscillatory velocity. For both steady and oscillatory flows, the method provides excellent agreement with FIDAP simulation results, even at locations close to the surface of a cylinder. In contrast to step-like solutions produced using the "bounce-back" condition, the proposed condition gives close agreement with the smooth FIDAP predictions. Computed drag forces with the proposed condition exhibit apparent quadratic convergence with grid refinement rather than the linear convergence exhibited by other LB boundary conditions.

We present a model for treating solid boundaries of a DPD fluid. The basic idea is to model the stick boundary conditions by assuming that a layer of DPD particles is stuck on the boundary. By taking a continuum limit of this layer effective dissipative and stochastic forces on the fluid DPD particles are obtained. The boundary model is tested by a simulation of planar Couette flow which allows the performance of vicosimetric measurements. We analyze the conditions that ensure a proper stick boundary condition for an impenetrable wall, comparing with previous methods used.

The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions, from two to five. The first two cumulants and the exponents for the universal scaling functions are shown to have simple power law variations with the dimensionality. The cases where multiple spanning clusters occur are discussed separately and compared.

Boundary conditions in a recently-proposed finite volume lattice Boltzmann method are discussed. Numerical simulations for simple shear flow indicate that the extrapolation and the half-covolume techniques for the boundary conditions are workable in conjunction with the finite volume lattice Boltzmann method for arbitrary meshes.

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm–Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.

We calculate the quantum statistical force acting on a partition wall that divides a one-dimensional box into two halves. The two half boxes containing the same (fixed) number of noninteracting bosons are kept at the same temperature, and admit the same boundary conditions at the outer walls; the only difference is the distinct boundary conditions imposed at the two sides of the partition wall. The net force acting on the partition wall is nonzero at zero temperature and remains almost constant for low temperatures. As the temperature increases, the force starts to decrease considerably, but after reaching a minimum it starts to increase, and tends to infinity with a square-root-of-temperature asympotics. This example demonstrates clearly that distinct boundary conditions cause remarkable physical effects for quantum systems.