Variational Formulation Research Articles

Variational Structures Beyond Gradient Flows: a Macroscopic Fluctuation-Theory Perspective

Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the density of the particle system. While large deviations can be studied in considerable generality, these variational structures are often restricted to systems in detailed balance. Using insights from macroscopic fluctuation theory, in this work we aim to generalise this variational connection beyond dissipative systems by augmenting densities with fluxes, which encode non-dissipative effects. Our main contribution is an abstract theory, which for a given flux-density cost and a quasipotential, provides a decomposition into dissipative and non-dissipative components and a generalised orthogonality relation between them. We then apply this abstract theory to various stochastic particle systems—independent copies of jump processes, zero-range processes, chemical-reaction networks in complex balance and lattice-gas models—without assuming detailed balance. For macroscopic equations arising out of these particle systems, we derive new variational formulations that generalise the classical gradient-flow formulation.

Pevesindo Visual Identity Design

<p class="5Abstract">PT Alastri Teguh International (PT ATI) is the leading distributor of the Natapon and Genius brands that manage building materials from polyvinyl chloride (PVC). Using a complete trading system to market PVC ceiling products in the south Sulawesi region makes product price stability unstable. Therefore, PT ATI created a new brand called Pevesindo, aimed at managing new businesses in the Java area and being a differentiator from the previous brands (Natapon and Genius). Pevesindo requires a visual identity with consistent and precise application. In order to support the company's image to make it easier for people to remember and recognize Pevesindo. This design uses a qualitative approach by adapting the Double Diamond design model from the Design Council. It has four stages that help the design process: Discover and Define (a research process that refers to problems), Discover and Deliver (the process of execution to the final result). The data obtained will be analyzed using a SWOT analysis. The resulting design is visual identity in the form of logos, typography, color variations, supergraphics, brand guidelines, and examples of the application of visual identity to the media to be used.</p>

A quasi-static model of a thermoelastic body reinforced by a thin thermoelastic inclusion

The problem of description of quasi-static behavior is studied for a planar thermoelastic body incorporating an inhomogeneity, which geometrically is a strip with a small cross-section. This problem contains a small positive parameter δ describing the thickness of the inhomogeneity, i.e., the size of the cross-section. Relying on the variational formulation of the problem, we investigate the behavior of solutions as δ tends to zero. As the result, by the version of the method of formal asymptotic expansions, we derive a closed limit model in which the inhomogeneity is thin (of zero width). After this, using the Galerkin method and the classical techniques of derivation of energy estimates, we prove existence, uniqueness, and stability of a weak solution to this model.

Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale.

Multiconfigurational pair-density functional theory (MC-PDFT) offers a promising solution to the challenges faced by traditional density functional theory (DFT) in addressing molecular systems containing transition metals, open-shells, or strong correlations in general. By utilizing both the density and on-top pair-density, MC-PDFT can make use of a more flexible multiconfigurational wave function to capture the necessary static correlation, while the pair-density functional also includes the effect of dynamic correlation. So far, MC-PDFT has been used after a multiconfigurational self-consistent field (MCSCF) step, using the orbitals and configuration interaction coefficients from the converged MCSCF wave function to compute PDFT energies and properties. Here, instead, we propose to perform a direct optimization of the wave function using the pair-density functionals, resulting in a variational formulation of MC-PDFT. We derive the expressions for the wave function gradient and illustrate their similarity to standard MCSCF equations. Furthermore, we illustrate the accuracy on a set of singlet-triplet gaps as well as dissociation curves. Our findings highlight one of MC-PDFT's standout features: a reduced dependency on the active space size compared to conventional multiconfigurational wave function methodologies. Additionally, we show that the computational cost of MC-PDFT is potentially lower than MCSCF and often on-par with standard Kohn-Sham DFT, which is demonstrated by performing a MC-PDFT calculation of the entire ferredoxin protein with 1447 atoms and nearly 12000 basis functions.

Bahasa Gaul di Media Sosial: Kajian Morfologi

This study aims to analyze the use of slang language on social media and its connection to standard language. The method used is qualitative descriptive with data analysis techniques through observation and field notes. Linguistic theories, especially morphology and syntax theories, are used in this research. The results show that the use of slang language on social media is connected to standard language, both in terms of morphology and syntax. Although slang language contains many loanwords from foreign languages and uses many abbreviations or acronyms, its usage has its own rules that follow the general structure of the Indonesian language. Therefore, slang language on social media can be considered as a form of language variation or style used by people in social interactions on social media.

Data-driven analysis of structural instabilities in electroactive polymer bilayers based on a variational saddle-point principle

In this work, we use a data-driven approach to model the onset of wrinkling in composite dielectric elastomer (DE) bilayer structures that are subjected to combined electro-mechanical loading conditions. Specifically, the critical surface-charge density required to activate wrinkling and the resulting number of half-waves are determined as functions of the tunable geometrical and material features of the DE bilayer using supervised machine learning (ML) models. The required data for the ML surrogates is generated using a finite-element-based framework for structural stability analysis of the DE bilayer, which is rooted in a variational saddle-point formulation for non-linear electro-elastostatics. Within the considered broad design space for the DE bilayer, the data points are sampled according to a Latin-hypercube-type design, following which training and test datasets containing the values of the target variables for the sampled input-feature vectors are generated using the adopted finite-element framework. Subsequently, we implement and compare the capabilities of different ML models to capture accurately the non-linear dependence of the wrinkling characteristics on the tunable features of the DE bilayer.

Variational formulation of thermomechanical problems

This article proposes that a 4D space-time continuum is used for building variational thermomechanical continuum models. In order to identify physical constants in reversible processes, physically justified hypotheses were formulated. They are the hypotheses of complementary shear stress, classical dependence of momentum on velocity, and heat flow potentiality (generalized Maxwell–Cattaneo law). The Duhamel–Neumann law was assumed to be classical. In the considered model, the generalized Maxwell–Cattaneo and Duhamel–Neumann laws were not introduced phenomenologically. They were derived from the compatibility equations by excluding thermal potential from the constitutive equations for temperature, heat flow, and pressure. Dissipation channels were considered as the simplest non-integrable variational forms, which are linear in the variations of arguments. As a result, a variational principle that generalizes L.I. Sedov’s principle was developed. It is a consequence of the virtual work principle and termed as the difference between the variation of the Lagrangian of reversible thermomechanical processes and the algebraic sum of dissipation channels. It was proved that for the classical thermomechanical processes, with second-order differential equations, there can only exist six dissipation channels. Two of them determine dissipation in an uncoupled system – in the equations of motion and heat balance. The remaining four channels define coupling effects in coupled problems of dissipative thermomechanics.

How Little and Meng’s Objective Approach Fails in Democracies

Little and Meng (L&M) (2023) question the prevailing narrative of widespread democratic backsliding by showing that various objective indicators of democracy are flat over time. However, because recent democratic decline is concentrated in democracies, the objective indicators can accurately test for backsliding only if they can track democratic quality within democracies. This response article shows that they cannot, for conceptual and empirical reasons. The indicators generally can distinguish democracies from autocracies but are blind to variation in quality within democracies. L&M, therefore, are showing that one form of variation in democracy is stagnant but are systematically missing the very type of variation that has most informed current warnings about backsliding.

Full weak Galerkin finite element discretizations for poroelasticity problems in the primal formulation

This paper develops novel finite element solvers for linear poroelasticity problems on quadrilateral meshes. These solvers are based on the primal formulations of linear elasticity and Darcy flow. Specifically, the fluid pressure and solid displacement are approximated by scalar- or vector-valued polynomials of degree k≥0 separately in element interiors and on edges. The discrete weak gradients of these shape functions are established in the broken (vector- or matrix-version) Arbogast–Correa spaces for approximations of the classical gradients in the variational forms. These weak Galerkin spatial discretizations are combined with the implicit Euler or Crank–Nicolson temporal discretizations to develop locking-free numerical solvers that have optimal order (k+1) convergence rates in pressure, velocity, displacement, stress, and dilation. Rigorous analysis is presented and illustrated by numerical experiments on popular test cases.

Corticosterone Contributes to Diet-Induced Reprogramming of Post-Metamorphic Behavior in Spadefoot Toads.

Stressful experiences in early life can have phenotypic effects that persist into, or manifest during, adulthood. In vertebrates, such carryover effects can be driven by stress-induced secretion of glucocorticoid hormones, such as corticosterone, which can lead to developmental reprogramming of hypothalamic-pituitary-adrenal/interrenal axis activity and behavior. Nutritional stress in the form of early life nutrient restriction is well known to modify later life behaviors and stress activity through corticosterone-related mechanisms. However, it is not known whether corticosterone is also mechanistically involved in carryover effects induced by a different form of nutritional variation: the use of alternate or entirely novel types of dietary resources. The plains spadefoot (Spea bombifrons) presents an excellent system for testing this question, since larvae of this species have evolved to use 2 alternate diet types: an ancestral detritus-based diet and a more novel diet of live shrimp. While previous work has shown that feeding on the novel shrimp diet influences juvenile (i.e., post-metamorphic) behavior and corticosterone levels, it is unclear whether these diet-induced carryover effects are mediated by diet-induced corticosterone itself. To test for the mechanistic role of corticosterone in diet-induced carryover effects, we experimentally treated S. bombifrons larvae with exogenous corticosterone and measured subsequent effects on juvenile behavior and corticosterone levels. We found that while shrimp-fed larvae had elevated corticosterone levels, treatment of larvae with corticosterone itself had effects on juvenile behavior that partially resembled those carryover effects induced by the shrimp diet, such as altered food seeking and higher locomotor activity. However, unlike carryover effects caused by the shrimp diet, larval corticosterone exposure did not affect juvenile corticosterone levels. Overall, our study shows that corticosterone-related mechanisms are likely involved in carryover effects induced by a novel diet, yet such diet-induced carryover effects are not driven by corticosterone alone.

VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM

Every shallow-water wave propagates along a fractal boundary, and its mathematical model cannot be precisely represented by integer dimensions. In this study, we investigate a coupled fractal–fractional KdV system moving along an irregular boundary within the framework of variational theory, which is commonly employed to derive governing equations. However, not every fractal–fractional differential equation can be formulated using variational principles. The semi-inverse method proves to be challenging in finding an appropriate variational principle for nonlinear problems and eliminating extraneous components from the studied model. We consider the coupled fractal–fractional KdV system with arbitrary coefficients and establish its variational formulation to unveil the remarkable insights into the energy structure of the model and interrelationships among coefficients. Encouraging results are obtained for this coupled KdV system.

Solitary wave solutions of the Navier-Stokes equations by He's variational method

Existence of variational principles for Navier-Stokes equations has been discussing for hundreds of years, but it has not yet been solved. In this study, a new perspective is proposed, which uses a traveling wave transform, so that a variational formulation can be established. Furthermore, the solitary wave solutions are solved by He?s variational method.

APPLICATION OF VARIATIONAL PRINCIPLE AND FRACTAL COMPLEX TRANSFORMATION TO (3+1)-DIMENSIONAL FRACTAL POTENTIAL-YTSF EQUATION

This paper focuses on the numerical investigation of the fractal modification of the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation. A variational approach based on the two-scale fractal complex transformation and the variational principle is presented for solving this fractal equation. The fractal potential-YTSF equation can be transformed as the original potential-YTSF equation by means of the fractal complex transformation. Some fractal soliton-type solutions and fractal periodic wave solutions are provided by using the variational principle proposed by He, which are not touched in the existing literature. Some remarks about the variational formulation and the wave solutions for the original potential-YTSF equation by Manafian et al. [East Asian J. Appl. Math. 10(3) (2020) 549–565] are also given. Numerical results of the fractal wave solutions with different fractal dimensions and amplitudes are presented to show the propagation behavior.

Simulation of crack propagation in piping components using phase field approach

Understanding the fracture behaviour in pipelines transporting steam and other resources is vital for its longevity and structural integrity. The prediction of crack initiation and propagation, involving crack branching, and the nucleation of new cracks, etc. in fracture processes are challenging tasks. The phase field method (PFM), based on variational formulation, emerged as a competitive mathematical tool to address fracture mechanics problems. PFM does not require the presence of predefined cracks, handles the crack initiation and propagation within the same system. This feature provides an added advantage to PFM and overcomes the limitations of Griffith’s approach-based linear elastic fracture mechanics (LEFM). In the present work, simulation of the crack propagation in the piping components by employing phase field methodologies has been carried out. Two parameters namely; a phase field parameter (ϕ) that varies between 0 and 1 differentiating between broken and intact material, and a length scale parameter (l_0) that approximates the sharp crack into the diffused crack with exponential distribution are introduced in the mathematical modeling. Numerical modeling is solved using the staggered algorithm in three layered scheme defining the displacement field and phase field within a 3-D finite element framework and implemented in Abaqus via user-defined element (UEL) subroutine codes. PFM simulates the crack path and predicts the load-displacement response, which is validated with benchmark problems, and extended for piping components under monotonic loading. The proposed study accurately captures the crack growth behaviour as observed in experiments on SA312 Type 304LN stainless steel pipes and hence, demonstrated the robustness of the proposed formulation.

Variational Formulation and Numerical Simulation of Stochastic Rayleigh-Plesset Equation

Variational Formulation and Numerical Simulation of Stochastic Rayleigh-Plesset Equation

A remark on Gibbs measures with log-correlated Gaussian fields

Abstract We study Gibbs measures with log-correlated base Gaussian fields on the d-dimensional torus. In the defocusing case, the construction of such Gibbs measures follows from Nelson’s argument. In this paper, we consider the focusing case with a quartic interaction. Using the variational formulation, we prove nonnormalizability of the Gibbs measure. When $d = 2$ , our argument provides an alternative proof of the nonnormalizability result for the focusing $\Phi ^4_2$ -measure by Brydges and Slade (1996). Furthermore, we provide a precise rate of divergence, where the constant is characterized by the optimal constant for a certain Bernstein’s inequality on $\mathbb R^d$ . We also go over the construction of the focusing Gibbs measure with a cubic interaction. In the appendices, we present (a) nonnormalizability of the Gibbs measure for the two-dimensional Zakharov system and (b) the construction of focusing quartic Gibbs measures with smoother base Gaussian measures, showing a critical nature of the log-correlated Gibbs measure with a focusing quartic interaction.

Comparative evaluation of arch form among the Nepalese population: A morphological study.

The study aims to identify sexual dimorphic features in the arch patterns based on tooth arrangement patterns and the maxillary and mandibular arches using Euclidean Distance Matrix Analysis (EDMA). A total of 96 Nepalese subjects, aged 18 to 25 were assessed using casts and photographs. Thirteen landmarks representing the most facial portions of the proximal contact areas on the maxillary and mandibular casts were digitised. Seventy-eight possible, Euclidean distances between the 13 landmarks were calculated using the Analysis ToolPak of Microsoft Excel®. The male-to-female ratios of the corresponding distances were computed and ratios were compared to evaluate the arch form for variation in the genders, among the Nepalese population. Microsoft Excel Analysis ToolPak and SPSS 20.0 (IBM Chicago) were used to perform EDMA and an independent t-test to compare the significant differences between the two genders. The maxillary arch's largest ratio (1.008179001) was discovered near the location of the right and left lateral incisors, indicating that the anterior region may have experienced the greatest change. The posterior-molar region is where the smallest ratio was discovered, suggesting less variation. At the intercanine region, female arches were wider than male ones; however, at the interpremolar and intermolar sections, they were similar in width. Females' maxillary arches were discovered to be bigger antero-posteriorly than those of males. The highest ratio (1.014336113) in the mandibular arch was discovered at the intermolar area, suggesting that males had a larger mandibular posterior arch morphology. At the intercanine area, the breadth of the arch form was greater in males and nearly the same in females at the interpremolar and intermolar regions. Female mandibular arch forms were also discovered to be longer than those of males from the anterior to the posterior. The male and female arches in the Nepalese population were inferred to be different in size and shape. With references to the landmarks demonstrating such a shift, the EDMA established objectively the presence of square arch forms in Nepali males and tapering arch forms in Nepalese females.

Higher-order convergence analysis for interior and boundary layers in a semi-linear reaction-diffusion system networked by a $ k $-star graph with non-smooth source terms

<p>We investigated a nonlinear singularly perturbed elliptic reaction-diffusion coupled system having non-smooth data networked by a $ k $-star graph. We considered all possible boundary conditions at the free boundary located at the tail of the edge and imposed the continuity condition with Kirchhoff's junction law at the junction point of the $ k $-star graph to obtain a continuous solution for this coupled system. First, we showed the existence and uniqueness of the solution using the variational formulation approach. Then, we reformulated it into a minimization problem over a function space to conclude the uniqueness of the solution. For the approximation of the continuous problem, note that the upwind scheme for the flux condition at the free boundary leads to a parameter uniform first-order approximation. To obtain a higher-order uniform accuracy, we utilized a three-point scheme for first-order derivatives and a five-point approximation at the point of discontinuity. These approximations typically did not yield an M-matrix or strict diagonally dominant structure of the stiffness matrix. Hence, we provided a suitable transformation that could lead to a sufficient condition for preserving the strict diagonally dominant structure of the stiffness matrix. We performed a comprehensive convergence analysis to demonstrate the almost second-order uniform accuracy on each edge of the $ k $-star graph. Numerical experiments highly validate the theory on the $ k $-star graph.</p>

NUMERICAL AND ANALYTICAL INVESTIGATION OF THE J-INTEGRAL VALUE IN A DOUBLE CANTILEVER BEAM SAMPLE WITH AN EXTREMELY THIN ELASTIC-PLASTIC ADHESION LAYER

The loading of a double cantilever beam sample, which is a composition of cantilevers and an adhesive layer, is considered, which leads to deformation of the layer by normal rupture. The basis of the mathematical model describing the equilibrium of the composite is the variational equilibrium equation connecting the stresses averaged over the thickness of the layer and the stress-strain state of the cantilever by a linear parameter. The behavior of the cantilever is considered within the framework of a linearly elastic body, the adhesive layer is considered elastic-plastic without hardening. The composite is considered in a state of plane deformation. Assuming the fulfillment of the condition of complete plasticity of the equality of two principal stresses acting orthogonally to separation and elastic volumetric deformation, the constitutive relations of the behavior of the layer at the stage of elastoplastic deformation are obtained. Using the distribution of the displacement field according to the theory of Mindlin-Reisner plates, a system of ordinary differential equations, conjugation conditions for solutions, and boundary conditions are obtained from the variational formulation of the problem. It is shown that, depending on the ratio of the linear parameter and the height of the console, the characteristic equation of the corresponding homogeneous system of differential equations has both real and complex roots. The corresponding general solutions of the system are found. Based on the consideration of one region of elastoplastic deformations, an iterative procedure for finding the length of the plastic zone is proposed, taking into account the satisfaction of boundary conditions. From the solution of the problem for a given value of the linear parameter and a critical external load, the stress-strain state of the layer is found, on the basis of which the J-integral is calculated. It is shown that as the linear parameter tends to zero, the J-integral asymptotically tends to the value found in the framework of the linearly elastic behavior of the layer material. For a certain range of values of the linear parameter, the obtained solution was compared with the finite element solution of the 2D problem.

VARIATIONAL PRINCIPLE FOR A FRACTAL LUBRICATION PROBLEM

Micro/nanoscale lubrication must take into account the fractal profile of the shaft and bearing surfaces. A new fractal rheological model is proposed to describe the properties of the non-Newtonian fluid, and a fractal variational principle is established by the semi-inverse method, and finally the Lagrange multipliers can be found in the obtained variational formulation. This work provides a new fractal approach to nano/micro lubrication.