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A non-self-adjoint fourth-order differential operator with nonsmooth coefficients and periodic boundary conditions is considered. Results concerning the asymptotics of the spectrum of this operator are obtained. [ABSTRACT FROM AUTHOR]

In this work, we present simulations of the optical rotation (OR) for five molecular crystals at density functional theory level with periodic boundary conditions (DFT‐PBC). Calculations are compared with experimental measurements and show semi‐quantitative agreement with experimental data for three of the crystals: tartatic acid, benzil, and pentaerythritol. For the other two crystals, aspartic acid and glutamic acid, the calculated data are in qualitative agreement with, but two orders of magnitude smaller than, the experimental data. We provide some arguments that support the theoretical predictions and suggest that the experiments should be revisited. We also find that the position of H centers provided in experimental X‐ray data is not sufficiently reliable for simulating OR, and better results are obtained when H atoms are allowed to relax while keeping heavier elements fixed at the experimental positions. Comparison with molecular cluster calculations with a better functional and a larger basis set indicate that the role of intermolecular interactions (reproduced with the PBC technique) is as or more important than the choice of model chemistry. Despite the current limitations in the level of theory that can be employed, these simulations provide a promising avenue to investigate the effect of intermolecular interactions on this sensitive electronic property of molecules and materials. [ABSTRACT FROM AUTHOR]

In this paper, we study the solvability of one initial-boundary value problem for the Burgers equation with periodic boundary conditions in a nonlinearly degenerating domain. In this paper, we found an orthonormal basis for domains with time-varying boundaries. On this basis, we use the Faedo–Galerkin method to prove theorems about the unique solvability of the problem under consideration. We also present some numerical results in the form of graphs of solutions to the problem under study for various initial data. [ABSTRACT FROM AUTHOR]

In this article a FE2 shell model for thin and thick shells within a first order homogenization scheme is presented. A variational formulation for the two‐scale boundary value problem and the associated finite element formulation is developed. Constraints with 5 or 9 Lagrange parameters are derived which eliminate both rigid body movements and dependencies of the shear stiffness on the size of the representative volume elements (RVEs). At the bottom and top surface of the RVEs which extend through the total thickness of the shell stress boundary conditions are present. The periodic boundary conditions at the lateral surfaces are applied in such a way that particular membrane, bending and shear modes are not restrained. This is shown by means of a homogeneous RVE. The first of all linear formulation is extended to finite strain problems introducing transformation relations for the stress resultants and the material matrix. The transformations are performed at the Gauss points on macro level. Several boundary value problems including large deformations, stability and inelasticity are computed and compared with 3D reference solutions. [ABSTRACT FROM AUTHOR]

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This article deals with the development of an elastic tetragonal model for the 2D auxetic rotating units structures in the framework of orthogonal transformations. The existing anisotropy in the structure was first determined by numerical simulations on the samples with different pattern orientation angles. A suitable representative volume element (RVE), which correctly represents the mechanical properties of the whole structure both in macroscale and in microscale, was then proposed by implementation of the kinematic periodic boundary conditions. In the next step, with the help of the orthogonal transformations relations, an anisotropic elastic model was developed, which correctly reflects the present tetragonal symmetry in the structure. Finally, the model parameters were identified and validated with the help of the corresponding experiments [ABSTRACT FROM AUTHOR]

This paper is concerned with a phase-field model driven by interface diffusion, which is an elliptic and nonlinear degenerate parabolic coupled system arising in a theory of interface motion in the elastically deformable materials. Spinodal decomposition is a typical example for this motion. We shall study the global existence of weak solutions to this model with a general polynomial potential function via the Galerkin method. Moreover, we perform the numerical simulations to investigate the spinodal decomposition process of binary alloy by applying this model. [ABSTRACT FROM AUTHOR]

This article studies the inverse problem of determining the pressure and convolution kernel in an integro-differential Moore-Gibson-Thompson equation with initial, periodic boundary and integral overdetermination conditions on the rectangular domain. By Fourier method this problem is reduced to an equivalent integral equation and on based of Banach's fixed point argument in a suitably chosen function space, the local solvability of the problem is proven. Then, the found solutions are continued throughout the entire domain of definition of the unknowns. [ABSTRACT FROM AUTHOR]

We introduce a successive approximations method to study one fractional periodic boundary value problem of the Hilfer-Prabhakar type. The problem is associated to the corresponding Cauchy problem, whose solution depends on an unknown initial value. To find this value we numerically solve the so-called 'determining system' of algebraic or transcendental equations. As a result, we determine an approximate solution of the studied problem, written in a closed form. Finally, we evaluate efficiency of our method on a nonlinear numerical example. [ABSTRACT FROM AUTHOR]

Mathematical analysis is conducted on cyclical systems with goodwill in capitalization. Proportional goodwill vanishes with vanishing tangible value. Correspondingly, periodic boundary condition does not enable commercial utilization of the goodwill. Abandoning the periodic boundary condition enables commercial utilization of the goodwill. Even if a physical system is periodic, an agent can abandon the corresponding boundary condition by divesting. Example cases are shown in terms of boreal forestry systems. [ABSTRACT FROM AUTHOR]

In this work, we focus on investigating the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. By extending the framework of the technique based on well-ordered coupled lower and upper solutions, we guarantee the existence of solutions in a sector defined by these solutions. One notable aspect of our study is that the proposed approach unifies the existence results for the problems that have previously been discussed separately in the literature. To substantiate these findings, we have added three illustrative examples.

Mathematical analysis is conducted on cyclical systems with goodwill in capitalization. Proportional goodwill vanishes with vanishing tangible value. Correspondingly, periodic boundary condition does not enable commercial utilization of the goodwill. Abandoning the periodic boundary condition enables commercial utilization of the goodwill. Even if a physical system is periodic, an agent can abandon the corresponding boundary condition by divesting. Example cases are shown in terms of boreal forestry systems.

In this work, we focus on investigating the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. By extending the framework of the technique based on well-ordered coupled lower and upper solutions, we guarantee the existence of solutions in a sector defined by these solutions. One notable aspect of our study is that the proposed approach unifies the existence results for the problems that have previously been discussed separately in the literature. To substantiate these findings, we have added three illustrative examples. [ABSTRACT FROM AUTHOR]

We give estimates for the eigenvalues of nonself-adjoint Sturm–Liouville operators with periodic and antiperiodic boundary conditions for the special potential that is a PT-symmetric optical potential, especially when or equally . We provide some useful equations for calculating the periodic and antiperiodic eigenvalues. We even approximate complex eigenvalues by the roots of some polynomials derived from some iteration formulas. Moreover, we give a numerical example with error analysis. [ABSTRACT FROM AUTHOR]

Novel analytical solutions with closed-form expressions for the stress and displacement fields of short fiber reinforced composites (SFRCs) and analytical prediction of their effective thermo-elastic properties are presented. The cylindrical SFRC unit-cells with periodic boundary conditions are subjected to axial and transverse stresses as well as thermally induced residual stresses. By comparison with available numerical and analytical solutions, it is revealed that the present closed-form solutions provide accurate stress field variations as well as accurate predictions for the effective thermo-elastic properties of SFRCs in a split second, and thus, the developed model is much more computationally efficient than numerical methods. [ABSTRACT FROM AUTHOR]

Semi-flexible pavement (SFP) material is a composite comprising cement, coarse aggregates and asphalt mortar, which has complex mechanical properties. Traditional experimental methods struggle to accurately quantify the effect of each phase and their interfaces on the SFP's mechanical properties. Micromechanical modelling based on finite element method offers a promising solution. In this study, a new micromechanical model for SFP is proposed, idealizing the material by representative volume elements. SFP mesostructure is represented as a simplified five element composite consisting of cement, asphalt mortar, aggregate, pore and cement-asphalt mortar interface. Periodic boundary conditions are used to simulate an infinite repetitive structure within a finite computational domain. The resulting model allows evaluating the stiffness and damage resistance of SFP in a computationally efficient manner. This model is utilized to explore the mechanical properties of SFPs and the results are compared with the experimental findings. The results show that the model captures the uniaxial compressive strength and stiffness for all materials examined. The model is further used to evaluate the effect of properties of individual elements of SFP on its stiffness and strength. The feasibility of using the proposed modelling approach to optimize the material design of SFP is discussed.

To explore the temperature distribution in width and depth of asphalt pavements with three different subgrade types, a numerical model is established. Based on actual meteorological data, the lateral temperature differences (LTDs) along the depth direction of pavement layers were analyzed under diurnal periodic thermal boundary conditions. Results reveal that the maximum LTD on the surface of a part-cut part-fill subgrade roadbed structure, as represented by a mountainous road, can reach 6.3 °C and 10.8 °C during winter and summer, respectively. The LTDs vary periodically with the boundary conditions. The LTDs on the road surface with high solar radiation in summer are 2.6–7.6 °C higher than those in winter. The influence ranges of the LTDs along the width direction of the road in winter and summer are 0–300 mm and 0–350 mm, respectively. This study provides a more precise method for studying the temperature field of road structures, which is helpful in analysing the pavement damage caused by thermal stress, etc. It also provides the necessary reference for the practical implementation of new technologies in the fields of asphalt pavement thermal energy storage systems and asphalt pavement temperature difference power generation.

In this paper, we introduced a reproducing kernel space which is a particular class of Hilbert space. We discuss various properties of the reproducing kernel. In particular, our aim is to construct kernel in reproducing kernel Hilbert space of the specific function space (Sobolev space) with the improved inner product and norm. Also, we derive the reproducing kernel for periodic boundary conditions. [ABSTRACT FROM AUTHOR]

Plane self-lubricating fabric liner is the research object, and the purpose is to study the effects and damage propagation behavior of each component material at different stages under out-of-plane compression loading. Firstly, the representative volume cell (RVC) model of woven cell with twill liner is established; Based on the 3D Hashin initial failure criteria and exponential damage evolution model, the user material subroutine (UMAT) of progressive damage has been written, which includes three component materials; Then, the periodic boundary conditions are added to the woven cell using a Python script, and the numerical analysis of the liner compression and the damage process was conducted, so we can get the damage state, damage propagation patterns and their rules of constituent materials under different loads. The research shows that: combining the progressive damage model and the numerical simulation with the periodic boundary conditions, the failure behavior of self-lubricating fabric liner under out-of-plane compression can be revealed, and the analytical method can provide effective support for developing high performance self-lubricating fabric liner. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new generalized result to study the existence of solutions of nonlinear fractional boundary value problems (FBVPs). The proposed results unify the existence criteria of certain FBVPs including periodic and antiperiodic as special cases that have been previously studied separately in the literature. The method we employ is topological in its nature and manifests themselves in the forms of differential inequalities (lower and upper solutions, and coupled lower and upper solutions (CLUSs)). Two examples are given to demonstrate the applicability of the developed theoretical results. [ABSTRACT FROM AUTHOR]

We analyze here a finite element space semidiscretization of the Allen-Cahn/Cahn-Hilliard system coupled with heat equation and based on the Maxwell-Cattaneo law. We prove that the semidiscrete solution converges weakly to the continuous solution as the discretization parameter tends to 0. We obtain optimal a priori error estimates in energy norm and related norms, assuming enough regularity on the solution. We also show that the semidiscrete solution converges to an equilibrium as time goes to infinity. [ABSTRACT FROM AUTHOR]

The periodic nature of stream-wise flow occurs in a cooling channel so frequently due to the multiple heat sources in electronic equipment, demanding the creation of an effective technique to improve the heat-cooling convection. This work explores thermal convection enhancement in a heated-block duct for periodic boundary conditions using the element-by-element (EBE) treatment in a semi-implicit projection finite element method (FEM) through a preconditioned conjugate gradient (PCG) solver. The effects of changing the Reynolds numbers (100, 175, and 250) on rectangular cylinders installed in the channel under periodic boundary conditions were studied using time-mean Nusselt number enhancement, friction factor enhancement, and thermal performance coefficient. The results show that the rectangular cylinders installed stream-wise above an upstream block promote thermal convection in the heated-block duct due to modifying the flow of no cylinders. However, increasing the number of rectangular cylinders increases the friction factor enhancement. As a result, the case for periodic boundary conditions with a rectangular cylinder above every two blocks has the best thermal performance coefficient. [ABSTRACT FROM AUTHOR]

We study a boundary value problem for a Caputo‐type fractional differential equation subjected to periodic boundary conditions. For an auxiliary problem with the simplified right‐hand side, we explicitly construct its unique solution. In addition, based on the theory of the topological index, we prove existence of at least one solution to the original problem. [ABSTRACT FROM AUTHOR]

A fourth order differential operator with eigenvalue parameter dependent and periodic boundary conditions is considered. This problem is realized by an operator polynomial with self-adjoint operators. The eigenvalues are investigated and their asymptotics are provided. [ABSTRACT FROM AUTHOR]

The aqueous solubility of solid-state pharmaceuticals can often be enhanced by cocrystallization with a coformer to create a binary cocrystal with preferred physical properties. Greater understanding of the internal and external forces that dictate molecular structure and intermolecular packing arrangements enables more efficient design of new cocrystals. Low-frequency (sub-200 cm−1) Raman spectroscopy experiments and solid-state density functional theory simulations have been utilized together to investigate the crystal lattice vibrations of mycophenolic acid, an immunosuppressive drug, in its pure form and as a cocrystal with 2,2′-dipyridylamine. The lattice vibrations primarily consist of large-amplitude translations and rotations of the crystal components, thereby providing insights into the critical intermolecular forces governing cohesion of the molecular solids. The simulations reveal that despite mycophenolic acid having a significantly unfavorable conformation in the cocrystal as compared to the pure solid, the cocrystal exhibits greater thermodynamic stability over a wide temperature range. The energetic penalty due to the conformational strain is more than compensated for by the strong intermolecular forces between the drug and 2,2′-dipyridylamine. Quantifying the balance of internal and external energy factors in cocrystal formation indicates a path forward in the development of future mycophenolic acid cocrystals. [ABSTRACT FROM AUTHOR]

We propose in this paper an efficient algorithm based on the Fourier spectral-Galerkin approximation for the fourth-order elliptic equation with periodic boundary conditions and variable coefficients. First, by using the Lax-Milgram theorem, we prove the existence and uniqueness of weak solution and its approximate solution. Then we define a high-dimensional $ L^2 $ projection operator and prove its approximation properties. Combined with Céa lemma, we further prove the error estimate of the approximate solution. In addition, from the Fourier basis function expansion and the properties of the tensor, we establish the equivalent matrix form based on tensor product for the discrete scheme. Finally, some numerical experiments are carried out to demonstrate the efficiency of the algorithm and correctness of the theoretical analysis.

In this article, we establish existence and multiplicity results for first-order Stieltjes differential equations satisfying a periodic boundary condition or an initial value condition. No monotonicity condition involving the right-hand side ff is imposed at the discontinuity points of the derivator gg. Our results rely on the fixed point index theory and new notions of strict lower and upper solutions. An application to a population model with an extreme event is presented to study the persistence of a species.

Our main concern in this study is to present the generalized results to investigate the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. The framework of the presented results relies on the lower and upper solutions approach which allows us to ensure the existence of solutions in a sector defined by well-ordered coupled lower and upper solutions. It is worth mentioning that the presented results unify the existence criteria of certain problems which were treated on a case-by-case basis in the literature. Two examples are supplied to support the results.

The present work describes a new approach for the design of a Frequency-Selective Surface (FSS) in the context of frequency filters to increase isolation between two vehicle-borne antennas. A compact FSS design based on nested square meandered resonators is optimized for multifrequency operation. Furthermore, a design workflow is proposed. In general, the measurement of low-profile FSS does not correspond to simulation through Floquet modes based on periodic boundary conditions due to the lack of uniformity of mutual coupling among the FSS unit cells. The proposed method demonstrates the agreement between the infinite simulation and the measurement of the finite prototype once a convenient scale factor is applied, which facilitates the design workflow. In this case, an FSS is used as an efficient filter to increase the isolation between antennas by 6 dB in three representative bands (3GPP, WiFI I and II). In this way, multifrequency antennas can be placed at approximately half their actual distance with the same performance in spatial-constrained vehicular environments. [ABSTRACT FROM AUTHOR]

Laser flash analysis (LFA) is an advantageous transient method, widely used for measuring thermal diffusivity of solid materials nowadays. In this paper, the thermal conductivity of graphite film enhanced carbon fiber composite was measured by LFA and the results show an unusual size-dependent effect which was considered to be due to violation of homogeneous assumptions. To investigate the size effect, numerical analyses based on the representative volume element (RVE) models were implemented to evaluate the thermal conductivities of composites with periodic microstructures. Transient periodic boundary conditions (PBCs) were proposed and applied to the RVEs for simulating the LFA. Transient simulative results obtained by applying PBCs verify the size effect and are in better agreement with the experimental data than those obtained by applying conventional adiabatic conditions. Moreover, the classical steady-state analyses on RVEs were performed for comparison. The reason for size effect was discussed in details. The present work expands the application scope of LFA to measuring thermal conductivity of complex composite and provides a perception of discreetly selecting specimen size and modifying the general LFA technique. [ABSTRACT FROM AUTHOR]

A common choice for multiscale modeling of the mechanical response of composites is to use periodic boundary conditions (PBCs) on square and cubical representative volume elements (RVEs). However, when strain localization occurs in the micromodel, these PBCs are unable to reproduce the transverse isotropy of composite materials with a random microstructure. Existing remedies to alleviate this issue have been proposed in literature by either rotating or shifting the periodicity constraints. However, this results in a mismatch of the microstructure on opposing edges which may prevent cracks to cross the boundary and consequently limit the supported localization angles. Furthermore, in absence of a strategy that ensures a single localization band to arise in a fracturing RVE, it is difficult to formulate a generic expression for the length scale parameter that is used to regulate the energy dissipation, which plays an important role in obtaining RVE‐size objective results. As an alternative to square (or cubical) RVEs, circular (or spherical) RVEs have been proposed in literature since they provide a response which is independent of the orientation due to shape of the RVE. However, it is shown in this work that the existing formulation with straightforward application of PBCs on a circular RVE fails to predict the correct softening behavior, due to over‐constraining when cracks reach the boundary. Therefore, a new formulation of PBCs on a circular RVE is proposed, which allows for a single fully developed localization band under arbitrary angle. The performance of the new formulation is tested with a series of simulations where macroscopic strains are imposed under varying orientations. It is demonstrated that the circular RVE with the new formulation of PBCs successfully predicts a transversely isotropic response with full softening without the issue of mismatching microstructure as with previously developed remedies for the square RVE. In addition, it is shown that the length scale parameter is well‐defined and independent of the orientation of the circular RVE. [ABSTRACT FROM AUTHOR]

This paper presents some spectral properties of the Sturm-Liouville equation associated with periodic boundary conditions and additional transmission conditions at one interior singular point. We derived asymptotic formulas for the eigenvalues of the considered problem. Note that the problem under consideration has not been investigated previously. To illustrate the originality of the results we constructed a simple example of a periodic Sturm-Liouville problem with transmission conditions, whose eigenvalues may not be simple. [ABSTRACT FROM AUTHOR]

The inertial focusing characteristics of particles in laminar flow pipes with high Re numbers were studied based on the “relative motion model”. In order to solve the problem of long pipes with high Re number flow, periodic boundary conditions were imposed on the inlet and outlet of the pipe. The research results show that the use of periodic boundary conditions can effectively reduce the computational, and the mechanical properties of particles in high Re flow can be calculated by using L=4D pipe. The difference from the low Re number is that as the Re number continues to increase, the lift force of the particles in the radial direction is no longer distributed as a parabola. The lift curve has a concave area between r+ =0.5 ~ 0.7, and there is a tendency for a new inertial focus point to appear in this section. By means of particles of a+ =1/17 for Re > 1 000, this new focus point position is solvable. In addition, in the analysis of the flow field, a secondary flow occurs around the particle, and its intensity gradually increases with the Re number and the closeness of the particle to the wall. The generation of the secondary flow affects the spatial distribution of the particle lift. [ABSTRACT FROM AUTHOR]

In this paper, it is studied the asymptotic expression of fourth order differential operator with periodic boundary conditions. For this operator, it is also considered conjugate boundary conditions at x=0 which shows discontinuity. For this purpose, firstly asymptotic expression of solutions areobtained. Then by using the the asymptotic formulas of fundamental solutions, asymptotic expression of eigenvalues and eigenfunctions are presented. It is also dealt with the asymptotic expression of same operator with antiperiodic boundary conditions and conjugate conditions [ABSTRACT FROM AUTHOR]

This paper introduces a new method to impose the periodic boundary conditions on the arbitrary mesh when we use the edge finite element method. By using the Floquet theorem, we reduce the analysis of an infinite bi-periodic structure to an elementary cell with pseudo-periodic conditions on the lateral sides. In this method, we establish a relationship between the electric field circulation along an edge on a face and the circulation of the associated edges on the opposite face. After that, we introduce periodic relations in the finite element system. To show the possibilities of the proposed method, we present two numerical studies and the obtained numerical results are compared to those produced by the existing methods. [ABSTRACT FROM AUTHOR]

Our main concern in this study is to present the generalized results to investigate the existence of solutions to nonlinear fractional boundary value problems (FBVPs) with generalized nonlinear boundary conditions. The framework of the presented results relies on the lower and upper solutions approach which allows us to ensure the existence of solutions in a sector defined by well-ordered coupled lower and upper solutions. It is worth mentioning that the presented results unify the existence criteria of certain problems which were treated on a case-by-case basis in the literature. Two examples are supplied to support the results. [ABSTRACT FROM AUTHOR]

Strain localization is one of the key phenomena which has been extensively studied in geomaterials and for other kinds of materials including metals and polymers. This well-known phenomenon appears when structure/material is closed to failure. Numerous theoretical, experimental, and numerical studies have been dedicated to this subject for a long while. In the numerical aspect, strain localization inside periodic granular assembly has not been well studied in the literature. In this paper, we investigate the occurrence and development of strain localization within a dense cohesive-frictional granular assembly with high coordination number under bi-periodic boundary conditions by Discrete Element Modeling (DEM). The granular assembly is composed of 2D circular particles and subjected to biaxial loading scheme with constant lateral pressure. The results show that the formation of shear bands is of periodic type, consistent with the boundary conditions used. The occurrence and development of the shear band are originated from the irreversible loss of cohesive contacts. The latter is viewed as micro-cracking in the cohesive-frictional granular media, which is highly concentrated in the periodic shear zones and thus related to the strain localization observed at the sample scale. Finally, we also show that the strain localization is in perfect agreement with the kinematic field, displayed in terms of displacement fluctuation.

The necessary and sufficient conditions are given for a sequence of complex numbers to be the periodic (or antiperiodic) spectrum of non-self-adjoint Dirac operator. [ABSTRACT FROM AUTHOR]