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We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on R Λ N , Λ N = [ - N , N ] d ∩ Z d with Hamiltonian H N (ϕ) = 1 4 d ∑ x ∼ y (ϕ (x) - ϕ (y)) 2 - ∑ x ∈ Λ N η (x) ϕ (x) and 0-boundary conditions. { η (x) } x ∈ Z d is a family of i.i.d. symmetric random variables. We study how the typical maximal height of a random interface is modified by the addition of quenched bulk disorder. We show that the asymptotic behavior of the maximum changes depending on the tail behavior of the random variable η (x) when d ≥ 5 . In particular, we identify the leading order asymptotics of the maximum. [ABSTRACT FROM AUTHOR]

This study proposes a new approach to reformulate the method of difference potentials (DPM) for linear interface problems whose solutions or their derivatives may be discontinuous due to singular sources across the interface. Eliminating the need to construct and solve the overdetermined system, which is required in the standard DPM, is the main advantage of this efficient reformulation of the difference potentials method (ERDPM), which decreases the computational cost and complexity of the method for governing interface problems. We use the proposed method to solve the steady-state convection–diffusion equation in two-dimensional geometries. Numerical results are obtained by ERDPM and compared with solutions obtained by DPM to validate the robustness, accuracy, convergence rates, and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Failure mode and effect analysis (FMEA) is a reliability analysis and risk management technique used to analyze the potential causes of system failure modes and their impact on system performance and has been used in many fields. However, the traditional FMEA model often ignores the weight of risk factors and their internal relationship in an uncertain setting. To compensate for the above shortcomings, this article proposes a new FMEA model for risk prioritization by combining the Hamy mean operator, logarithmic percentage change-driven objective weighting (LOPCOW) model, and additive ratio assessment (ARAS) method under interval-valued Fermatean fuzzy (IVFF) environment. To begin with, novel IVFF operations based on Aczel–Alsina norms are defined. Then, some novel Hamy mean operators are proposed based on the defined operations including the IVFF Aczel–Alsina Hamy mean (IVFFAAHAM) operator, IVFF Aczel–Alsina weighted Hamy mean (IVFFAAWHAM) operator and their dual forms. The corresponding properties of these operators are also investigated. Further, the IVFF-LOPCOW method is proposed to find the weight of risk criteria and an improved ARAS method is propounded based on the presented operators for attaining the ranking of failure modes. Afterward, a novel FMEA model based on the integrated IVFF-LOPCOW-ARAS methodology is constructed, which can effectively determine the weight of experts and risk factors, as well as consider the interrelationship in the course of risk analysis. Lastly, a case about the risks in the R&D project of an industrial robot offline programming system is utilized to test the feasibility of the proposed FMEA model. The stability and advantages of the model are also investigated through sensitivity and comparison studies, respectively. [ABSTRACT FROM AUTHOR]

Soft sets ( S t S) theory provides a general mechanism for handling uncertainty based on the point of view of parameterization tools. The main theme of this manuscript is to extend the notion of Hamacher operators by establishing an interesting connection between two mathematical concepts S t S theory and q-rung orthopair fuzzy sets (q-ROFS). To be specific, we develop some new Hamacher operations for q-rung orthopair fuzzy soft sets (q-ROF S t S). In light of these operational laws, we further propose some q-rung orthopair fuzzy soft Hamacher aggregation operators, i.e., q-ROF soft Hamacher averaging and q-ROF soft Hamacher geometric aggregation operators, such as q-ROF soft Hamacher weighted averaging (q-ROF S t HWA), q-ROF soft Hamacher ordered weighted averaging (q-ROF S t HOWA) and q-ROF soft Hamacher hybrid averaging (q-ROF S t HHA) operators. Furthermore, based on Hamacher operator laws, we discuss some geometric aggregation operators such as q-ROF soft Hamacher weighted geometric (q-ROF S t HWG), q-ROF soft Hamacher ordered weighted geometric (q-ROF S t HOWG) and q-ROF soft Hamacher hybrid geometric (q-ROF S t HHG) operators. Meanwhile, the important properties of the developed operators are investigated in detail. Then, a technique for multi-criteria decision making and a stepwise algorithm for decision making are demonstrated by utilizing the proposed approach. Finally, a numerical example for the developed approach is presented and a comparative study of the investigated models with some existing methods is performed. The derived results demonstrate that the investigated models are more effective and useful than the existing approaches. [ABSTRACT FROM AUTHOR]

We consider scalar-valued variational models for pattern formation in helimagnetic compounds and in shape memory alloys. Precisely, we consider a non-convex multi-well bulk energy term on the unit square, which favors four gradients (± α , ± β) , regularized by a singular perturbation in terms of the total variation of the second derivative. We derive scaling laws for the minimal energy in the case of incompatible affine boundary conditions in terms of the singular perturbation parameter as well as the ratio α / β and the incompatibility of the boundary condition. We discuss how well-studied models for martensitic microstructures in shape-memory alloys arise as a limiting case, and relations between the different models in terms of scaling laws. In particular, we show that scaling regimes arise in which an interpolation between the rather different branching-type constructions in the spirit of Kohn and Müller (Commun Pure Appl Math 47(4):405–435, 1994) and Ginster and Zwicknagl (J Nonlinear Sci 33:20, 2023), respectively, occurs. A particular technical difficulty in the lower bounds arises from the fact that the energy scalings involve various logarithmic terms that we capture in matching upper and lower scaling bounds. [ABSTRACT FROM AUTHOR]

Particles deforming a soft matter medium interact through the deformation they create, like in the Cheerios effect. Bound by an elastic field, their interactions are essentially multi-body. Such particles may exhibit a liquid-gas phase separation. When the field correlation length is much larger than the size of the particles, the liquid phase is particularly sparse and compressible. Using a simple but realistic Gaussian model, we show that it behaves like a normal liquid with respect to the wetting phenomenon. [ABSTRACT FROM AUTHOR]

We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The results provide quantitative estimates, sharp up to multiplicative constants, in the following cases. It is shown that for real-valued random-field random surfaces of the ∇ ϕ type with a uniformly convex interaction potential: (i) The gradient of the surface delocalizes in dimensions 1 ≤ d ≤ 2 and localizes in dimensions d ≥ 3 . (ii) The surface delocalizes in dimensions 1 ≤ d ≤ 4 and localizes in dimensions d ≥ 5 . It is further shown that for the integer-valued random-field Gaussian free field: (i) The gradient of the surface delocalizes in dimensions d = 1 , 2 and localizes in dimensions d ≥ 3 . (ii) The surface delocalizes in dimensions d = 1 , 2 . (iii) The surface localizes in dimensions d ≥ 3 at low temperature and weak disorder strength. The behavior in dimensions d ≥ 3 at high temperature or strong disorder is left open. The proofs rely on several tools: Explicit identities satisfied by the expectation of the random surface, the Efron–Stein concentration inequality, a coupling argument for Langevin dynamics (originally due to Funaki and Spohn (Comm Math Phys 185(1): 1-36, 1997) and the Nash–Aronson estimate. [ABSTRACT FROM AUTHOR]

Atanassov presented the dominant notion of intuitionistic fuzzy sets which brought revolution in different fields of science since their inception. The operations of t-norm and t-conorm introduced by Dombi were known as Dombi operations and Dombi operational parameter possesses natural flexibility with the resilience of variability. The advantage of Dombi operational parameter is very important to express the experts' attitude in decision-making. This study aims to propose intuitionistic fuzzy rough TOPSIS method based on Dombi operations. For this, first we propose some new operational laws based on Dombi operations to aggregate averaging and geometric aggregation operators under the hybrid study of intuitionistic fuzzy sets and rough sets. On the proposed concept, we present intuitionistic fuzzy rough Dombi weighted averaging, intuitionistic fuzzy rough Dombi ordered weighted averaging, and intuitionistic fuzzy rough Dombi hybrid averaging operators. Moreover, on the developed concept, we present intuitionistic fuzzy rough Dombi weighted geometric, intuitionistic fuzzy rough Dombi ordered weighted geometric, and intuitionistic fuzzy rough Dombi hybrid geometric operators. The basic related properties of the developed operators are presented in detailed. Then the algorithm for MCGDM based on TOPSIS method for intuitionistic fuzzy rough Dombi averaging and geometric operators is presented. By applying accumulated geometric operator, the intuitionistic fuzzy rough numbers are converted into the intuitionistic fuzzy numbers. The massive outbreak of the pandemic COVID-19 promoted the challenging scenario for the world organizations including scientists, laboratories, and researchers to conduct special clinical treatment strategies to prevent the people from COVID-19 pandemic. Additionally, an illustrative example is proposed to solve MCGDM problem to diagnose the most severe patient of COVID-19 by applying TOPSIS. Finally, a comparative analysis of the developed model is presented with some existing methods which show the applicability and superiority of the developed model. [ABSTRACT FROM AUTHOR]

In this article, we propose and analyze a fully coupled, nonlinear, and energy-stable virtual element method (VEM) for solving the coupled Poisson–Nernst–Planck (PNP) and Navier–Stokes (NS) equations. These equations model microfluidic and electrochemical systems that include the diffuse transport of charged species within incompressible fluids coupled through electrostatic forces. A mixed VEM is employed to discretize the NS equations whereas classical VEM in primal form is used to discretize the PNP equations. The stability, existence and uniqueness of solution of the associated VEM are proved by fixed point theory. The global mass conservation and electric energy decay of the scheme are also established. Also, we rigorously derive unconditionally optimal error estimates for both the electrostatic potential and ionic concentrations of PNP equations in the L 2 and H 1 -norms, as well as for the velocity and pressure of NS equations in the L 2 , H 1 - and L 2 -norms, respectively. Finally, several numerical experiments are presented to support the theoretical analysis of convergence and to illustrate the satisfactory performance of the method in simulating the onset of electrokinetic instabilities in ionic fluids, and studying how they are influenced by different values of ion concentration and applied voltage. These tests are relevant in applications of water desalination. [ABSTRACT FROM AUTHOR]

We study pattern formation in magnetic compounds near the helimagnetic/ferromagnetic transition point in case of Dirichlet boundary conditions on the spin field. The energy functional is a continuum approximation of a J 1 - J 3 model and was recently derived in Cicalese et al. (SIAM J Math Anal 51: 4848–4893, 2019). It contains two parameters, one measuring the incompatibility of the boundary conditions and the other measuring the cost of changes between different chiralities. We prove the scaling law of the minimal energy in terms of these two parameters. The constructions from the upper bound indicate that in some regimes branching-type patterns form close to the boundary of the sample. [ABSTRACT FROM AUTHOR]

The continuum model related to the Winterbottom problem, i.e., the problem of determining the equilibrium shape of crystalline drops resting on a substrate, is derived in dimension two by means of a rigorous discrete-to-continuum passage by Γ -convergence of atomistic models taking into consideration the atomic interactions of the drop particles both among themselves and with the fixed substrate atoms. As a byproduct of the analysis, effective expressions for the drop surface anisotropy and the drop/substrate adhesion parameter appearing in the continuum model are characterized in terms of the atomistic potentials, which are chosen of Heitmann–Radin sticky-disk type. Furthermore, a threshold condition only depending on such potentials is determined distinguishing the wetting regime, where discrete minimizers are explicitly characterized as configurations contained in an infinitesimally thick layer, i.e., the wetting layer, on the substrate, from the dewetting regime. In the latter regime, also in view of a proven conservation of mass in the limit as the number of atoms tends to infinity, proper scalings of the minimizers of the atomistic models converge (up to extracting a subsequence and performing translations on the substrate surface) to a bounded minimizer of the Winterbottom continuum model satisfying the volume constraint. [ABSTRACT FROM AUTHOR]

In the present paper, we study the homogenization of a class of quasilinear elliptic problems in a two-component domain (one connected and the other a disconnected union of small sets) with a jump of the solution on the interface, proportional to the flux. We prescribe L 1 data and coefficient periodic matrix fields A(y, t) only bounded for bounded t, which implies that we cannot use the variational setting for our problem. We instead use the adapted framework of renormalized solution, where the solution is suitably defined, and does not belong to the H 1 Sobolev space but only their truncated functions are in H 1 . To study the homogenization of the problem, we use the periodic unfolding method, which we can only apply to the truncated solutions, which are in H 1 . Nevertheless, we are able to identify the homogenized problem, which also has only a renormalized solution. The main difficulty here is managing the boundary integral that results from the jump on the interface, and the study of the properties of the solution in the disconnected component. Conditions for the uniqueness of both problems, the oscillating one and the homogenized are also stated. [ABSTRACT FROM AUTHOR]

In this paper, we present a nonconforming immersed finite element method for solving elliptic optimal control problems with interfaces. The immersed finite element space is constructed based on the rotated-Q1 nonconforming finite elements with the integral-value degrees of freedom. The method can overcome the difficulties encountered by conforming immersed finite element method. We derive error estimates for the control, state and adjoint state in both energy and L 2 norms. Numerical results are reported to support the theoretical analysis. [ABSTRACT FROM AUTHOR]

In recent years, several numerical methods have been developed for differential equations with discontinuous coefficients, which are known as interface problems. Our aim is to introduce an efficient global meshless method for solving elliptic problems with arbitrary interface. Meshless methods based on infinitely smooth radial basis functions (RBFs) can achieve spectral convergence rate for solving partial differential equations. RBF-QR is a newly developed method which allows numerically stable computations with RBFs for all values of the free shape parameter ε . In this paper, an appropriate RBF-QR collocation technique is applied for two-dimensional elliptic interface problems, including Poisson, Helmholtz and elasticity problems. The Helmholtz interface problem is studied, by taking into account the fact that the solutions of such problems might be oscillatory. The elasticity interface problem is discussed as an application of elliptic interface problem in vector form. Several problems involving complex interface geometries and discontinuous variable coefficients are presented to confirm the efficiency and stability of RBF-QR method for this class of problems in the case of arbitrary small values of ε . [ABSTRACT FROM AUTHOR]

We consider the d (≥ 3) - dimensional lattice Gaussian free field on Λ N : = [ - N , N ] d ∩ Z d in the presence of a self-potential of the form U (r) = - b I (| r | ≤ a) , a > 0 , b ∈ R . When b > 0 , the potential attracts the field to the level around zero and is called square-well pinning. It is known that the field turns to be localized and massive for every a > 0 and b > 0 . In this paper, we consider the situation that the parameter b < 0 and self-potentials are imposed on Λ α N , α ∈ (0 , 1) . We prove that once we impose this weak repulsive potential from the level [ - a , a ] , most sites are located on the same side and the field is pushed to the same level when the original Gaussian field is conditioned to be positive everywhere, or negative everywhere with probability 1 2 , respectively. This result can be applied to show the similar path behavior for the disordered pinning model in the delocalized regime. [ABSTRACT FROM AUTHOR]

Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems numerically is the non-symmetric coupling of finite elements (FEM) and boundary elements (BEM) analyzed in [H. Egger, C. Erath and R. Schorr, On the nonsymmetric coupling method for parabolic-elliptic interface problems, SIAM J. Numer. Anal. 56 2018, 6, 3510–3533]. If, for example, the interior problem represents a fluid, this method is not appropriate since FEM in general lacks conservation of numerical fluxes and in case of convection dominance also stability. A possible remedy to guarantee both is the use of the vertex-centered finite volume method (FVM) with an upwind stabilization option. Thus, we propose a (non-symmetric) coupling of FVM and BEM for a semi-discretization of the underlying problem. For the subsequent time discretization we introduce two options: a variant of the backward Euler method which allows us to develop an analysis under minimal regularity assumptions and the classical backward Euler method. We analyze both, the semi-discrete and the fully-discrete system, in terms of convergence and error estimates. Some numerical examples illustrate the theoretical findings and give some ideas for practical applications. [ABSTRACT FROM AUTHOR]

The friction at the liquid-solid interfaces is widely involved in various phenomena ranging from nanometer to micrometer scales. By the molecular dynamic (MD) simulation, the friction properties of liquid-solid interfaces at the molecular level are calculated via the Green-Kubo relation. It is found that the system size will influence the value of the friction coefficient, especially for the solid surfaces with the larger polar charge. The value of the friction coefficient decreases with the increase in the system size and converges at large system sizes. The large polar charge will lead to a significant friction coefficient. However, the diffusion of water molecules on this surface is almost a constant, indicating that the diffusion coefficient seems to be independent of the system size and polar charge. This work provides insights for the selection of the system size in modeling the frictional properties of hydrophobic/hydrophilic surfaces. [ABSTRACT FROM AUTHOR]

We consider low-energy configurations for the Heitmann–Radin sticky discs functional, in the limit of diverging number of discs. More precisely, we renormalize the Heitmann–Radin potential by subtracting the minimal energy per particle, i.e. the so-called kissing number. For configurations whose energy scales like the perimeter, we prove a compactness result which shows the emergence of polycrystalline structures: The empirical measure converges to a set of finite perimeter, while a microscopic variable, representing the orientation of the underlying lattice, converges to a locally constant function. Whenever the limit configuration is a single crystal, i.e. it has constant orientation, we show that the Γ -limit is the anisotropic perimeter, corresponding to the Finsler metric determined by the orientation of the single crystal. [ABSTRACT FROM AUTHOR]

In this paper, we consider a time-dependent semilinear parabolic problem modeling the heat diffusion in a two-component composite. The domain has an ε -periodic interface, where the flux of the temperature is proportional to the jump of the temperature field by a factor of order ε γ . We determine the existence and uniqueness of the weak solution of the problem and use the periodic unfolding method to find the homogenization results. [ABSTRACT FROM AUTHOR]