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We prove that for each p ∈ (1 , ∞) the energy functional associated with the Dirichlet system - div (ϕ p (∇ u) ∇ u) = ∂ 1 F (u , v) in Ω , - div (ϕ p (∇ v) ∇ v) = ∂ 2 F (u , v) in Ω , u = v = 0 on ∂ Ω , admits at least one global, nonnegative minimizer (u p , v p) ∈ W 0 Φ p (Ω) × W 0 Φ p (Ω) which converges uniformly on Ω ¯ to (d Ω , d Ω) , as p → ∞ . Here Φ p (t) : = ∫ 0 t s ϕ p (s) d s and d Ω stands for the distance function to the boundary ∂ Ω . [ABSTRACT FROM AUTHOR]

This study establishes thermodynamic assumptions regarding the growth of condensation droplets and a mathematical formulation of droplet energy functionals. A model of the gas–liquid interface condensation rate based on kinetic theory is derived to clarify the relationship between condensation conditions and intermediate variables. The energy functional of a droplet, derived using the principle of least action, partially elucidates the inherent self-organizing growth laws of condensed droplets, enabling predictive modeling of the droplet's growth. Considering the effects of the condensation environment and droplet heat transfer mechanisms on droplet growth dynamics, we divide the process into three distinct stages, marked by critical thresholds of 105 nm3 and 1010 nm3. Our model effectively explains why the observed contact angle fails to reach the expected Wenzel contact angle. This research presents a detailed analysis of the factors affecting surface condensation and heat transfer. The predictions of our model have an error rate of less than 3% error compared to baseline experiments. Consequently, these insights can significantly contribute to and improve the design of condensation heat transfer surfaces for the phase-change heat sinks in microprocessor chips. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to develop a histogram equalization algorithm for color image contrast enhancement. Our idea is to propose a variational approach containing an energy functional to determine local transformations in the lightness (L) and chroma (C) channels of the CIE LCH color space such that the histograms in these two channels can be redistributed locally. In order to minimize the differences among the local transformation at the nearby pixel locations in each channel, the spatial regularization of the transformation is incorporated in the functional for the equalization process. The existence and uniqueness of the minimizer of the variational model can be shown. Experimental results are reported to show that the performance of the proposed models is competitive with the other compared methods for several testing images. [ABSTRACT FROM AUTHOR]

For some complex images, low contrast, intensity inhomogeneity, and blurred edges are common phenomena, which inevitably cause difficulties in image segmentation. As a popular image segmentation method, the active contour model (ACM) is often used to solve the above problems. However, the ACM is highly dependent on the initial evolving curves, which makes the model unstable and complex in the actual image segmentation. In this paper, a novel dual active contour model (DACM) is proposed to segment images, which integrates region and edge information to obtain accurate segmentation. Thereinto, the two contours are initialized and evolved simultaneously. The proposed DACM can use region-based and edge-based information, which can handle images with complex structures. For region-based DACM, uniformity among the object pixels and background difference is interlinked to provide an evolving force. Here, uniformity among the object pixels is constructed based on the color reward strategy. For edge-based DACM, the adjustable weighting parameter is set based on image gradient information of two evolving curves. The edge-based DACM can make the evolving curves move inward or outward adaptively. The proposed method is evaluated on various synthetic and real images and accurate segmentation results are obtained. Besides, the state-of-the-art methods are compared with the proposed DACM and an in-depth study of this novel method is given, which denotes that the proposed model can be applied to different types of complex image segmentation. [ABSTRACT FROM AUTHOR]

We study by variational methods a two-dimensional model of deformations of a Stieltjes string having localized interactions with the environment. In this model, the deviation of any point of the string from the equilibrium position under the action of an external force is characterized by two coordinates. We assume that the ends of the string are elastically fixed. Moreover, the movement of one of string ends is limited by a bounded, closed, convex set , lying in a plane perpendicular to the equilibrium position. Depending on the applied external force, this string end either remains an internal point of or touches the boundary of . This leads to a nonlinear boundary condition at the corresponding point. We establish the necessary and sufficient conditions for the extremum of the energy functional, prove the existence and uniqueness theorems of the solution; find an explicit formula for the solution and study its dependence on the size of the set . [ABSTRACT FROM AUTHOR]

This manuscript is concerned with the homogeneous Neumann initial-boundary problem for a susceptible-infected-susceptible model involving chemotactic movement of susceptibles away from infected individuals, as well as a mass action infection mechanism in its full quadratic strength. By constructing a quasi-energy functional on the basis of a suitable exploitation of a zero-order dissipative term together with the impact of diffusion, under an assumption on asymptotic smallness of the prescribed tactic sensitivity at large cell-densities a result on global existence of classical solutions emanating from initial data of arbitrary size is derived. [ABSTRACT FROM AUTHOR]

We prove the existence of the first eigenvalue and an associated eigenfunction with Dirichlet condition for the complex Monge–Ampère operator on a bounded strongly pseudoconvex domain in C n . We show that the eigenfunction is plurisubharmonic, smooth with bounded Laplacian in Ω and boundary values 0. Moreover it is unique up to a positive multiplicative constant. To this end, we follow the strategy used by P. L. Lions in the real case. However, we have to prove a new theorem on the existence of solutions for some special complex degenerate Monge–Ampère equations. This requires establishing new a priori estimates of the gradient and Laplacian of such solutions using methods and results of Caffarelli et al. (Commun Pure Appl Math 38(2):209–252, 1985) and Guan (Commun Anal Geom 6(4):687–703, 1998). Finally we provide a Pluripotential variational approach to the problem and using our new existence theorem, we prove a Rayleigh quotient type formula for the first eigenvalue of the complex Monge–Ampère operator. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the parabolic deformed Hermitian-Yang-Mills equation with hypercritical phase in a smooth domain \Omega \subset \mathbb {C}^{n}. By using J-functional, we are able to prove the convergence of solutions. As an application, we give an alternative proof of the Dirichlet problem for deformed Hermitian-Yang-Mills equation. [ABSTRACT FROM AUTHOR]

This study establishes thermodynamic assumptions regarding the growth of condensation droplets and a mathematical formulation of droplet energy functionals. A model of the gas–liquid interface condensation rate based on kinetic theory is derived to clarify the relationship between condensation conditions and intermediate variables. The energy functional of a droplet, derived using the principle of least action, partially elucidates the inherent self-organizing growth laws of condensed droplets, enabling predictive modeling of the droplet’s growth. Considering the effects of the condensation environment and droplet heat transfer mechanisms on droplet growth dynamics, we divide the process into three distinct stages, marked by critical thresholds of 105 nm3 and 1010 nm3. Our model effectively explains why the observed contact angle fails to reach the expected Wenzel contact angle. This research presents a detailed analysis of the factors affecting surface condensation and heat transfer. The predictions of our model have an error rate of less than 3% error compared to baseline experiments. Consequently, these insights can significantly contribute to and improve the design of condensation heat transfer surfaces for the phase-change heat sinks in microprocessor chips.

A qualitative study of nonlinear, 1D stochastic fractional wave equations with dissipative nonlinearities of power-law form is conducted on (t,x)∈[0,+∞)×D utt+σ2(−uxx)α−a1u+a2‖u‖L2(D)ρu−κut=b0∂W0∂t on (t,x)∈[0,+∞)×D with D=[0,L], where positive fractional α-powers of Laplace operator are allowed, perturbed by additive space–time random noise W0 with fairly general covariance operator Q with finite trace(Q)

This paper deals with a pseudo-parabolic equation involving p(x)-Laplacian and variable nonlinear sources. Firstly, we use the Faedo-Galerkin method to give the existence and uniqueness of weak solution in the Sobolev space with variable exponents. Secondly, in the frame of variational methods, we classify the blow-up and the global existence of solutions completely by using the initial energy, characterized with the mountain pass level, and Nehari energy. In the supercritical case, we construct suitable auxiliary functions to determine the quantitative conditions on the initial data for the existence of blow-up or global solutions. The results in this paper are compatible with the problems with constant exponents. Moreover, we give broader ranges of exponents of source and diffusion terms in the discussion of blow-up or global solutions. [ABSTRACT FROM AUTHOR]

Nonlinear stability of plane parallel convective shear flows of a binary fluid mixture heated and salted from below is investigated by generalized energy method. Through defining a new energy functional, a sufficient condition for unconditional nonlinear exponential stability of the basic motions is proved in the case of streamwise perturbation. The results in the paper have improved the results in the literature very well, and the restriction on Reynolds number is weaker than that in the literature. [ABSTRACT FROM AUTHOR]

We give a short survey on plurisubharmonic interpolation, with a focus on the possibility of connecting two given plurisubharmonic functions by plurisubharmonic geodesics. [ABSTRACT FROM AUTHOR]

In this paper, we propose a user-friendly integral inequality to study the coupled parabolic chemotaxis system with singular sensitivity under the Neumann boundary condition. Under a low diffusion rate, the classical solution of this system is uniformly bounded. Our proof replies on the construction of the energy functional containing ∫ Ω | v | 4 v 2 with v > 0 . It is noteworthy that the inequality used in the paper may be applied to study other chemotaxis systems. [ABSTRACT FROM AUTHOR]

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We propose an unconditionally gradient stable scheme for solving the Cahn–Hilliard equation with second‐order accuracy in time using the effective time‐step analysis. The conventional convex splitting scheme is one of the most well‐known methods for solving gradient flows, and it guarantees both energy stability and first‐order accuracy in time. Recently, there are some researches, which are extended to the second‐order accuracy; however, most of results provide the proof of energy stability for a modified (pseudo) energy or in a weak sense. In this paper, we prove the energy stability of the proposed method with respect to the Ginzburg–Landau free energy functional. Moreover, the unique solvability, mass conservation, and accuracy of the proposed scheme are also proven based on the convex splitting approach. The numerical experiments are presented to show convergence rate, mass conservation, energy stability, and phase separation are in good agreement with the theory. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of normalized solution to the following nonlinear mass super-critical Kirchhoff equation - a + b ∫ R N | ∇ u | 2 ▵ u + V (x) u + λ u = g (u) in R N 0 ≤ u ∈ H r 1 (R N) where a , b > 0 are constants, λ ∈ R , and V(x) satisfies appropriate assumptions; g has a mass super-critical growth when N = 3 , and g (u) = | u | p - 2 u with p ∈ (2 + 8 N , 2 ∗) , 2 ∗ = 2 N N - 2 when N ≥ 3 . Here, we prove the existence of ground state normalized solution via variational methods. [ABSTRACT FROM AUTHOR]

In this paper we handle the problem of filling the hole in the graphic of a surface by means of a patch that joins the original surface with C 1 -smoothness and fulfills an additional non-linear geometrical constraint regarding its area or its mean curvature at some points. Furthermore, we develop a technique to estimate the optimum area that the filling patch is expected to have that will allow us to determine optimum filling patches by means of a system of linear and quadratic equations. We present several numerical and graphical examples showing the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the present paper, we investigate a problem, describing the deformations process for the Stieltjes strings system located along a geometric star - shaped graph under the influence of an external force. The case when the force can be concentrated at separate points, including a node of the graph, is considered. The non-linear condition arises due to the presence of a limiter on the strings displacement in the node. Using variational methods, the necessary and sufficient conditions for the extremum of an energy functional are established; existence and uniqueness theorems for the solution are proved; an explicit formula for the solution is obtained; and the dependence solution on the length of the limiter is studied. [ABSTRACT FROM AUTHOR]

This work deals with the existence of at least one positive ground state solution for a stationary perturbed critical elliptic system with superlinear potential. Our problems involve the critical Sobolev constants which generate the lack of compactness in unbounded domains; we overcome such difficulty by using the concept of the Palais–Smale convergence. We make recourse to the Ekeland variational principle to show that our problem has a positive time-independent solution with positive energy as the total energy of the system. [ABSTRACT FROM AUTHOR]

Let \Omega be a smooth, bounded N-dimensional domain. For each p>N, let \Phi _{p} be an N-function satisfying p\Phi _{p}(t)\leq t\Phi _{p}^{\prime }(t) for all t>0, and let I_{p} be the energy functional associated with the equation -\Delta _{\Phi _{p}}u=f(u) in the Orlicz-Sobolev space W_{0}^{1,\Phi _{p}}(\Omega). We prove that I_{p} admits at least one global, nonnegative minimizer u_{p} which, as p\rightarrow \infty, converges uniformly on \overline {\Omega } to the distance function to the boundary \partial \Omega. [ABSTRACT FROM AUTHOR]

In this paper, a finite difference scheme is presented for the initial-boundary value problem for the two-dimensional nonlinear Fisher–Kolmogorov–Petrovski–Piskunov (Fisher–KPP) equation with mixed boundary conditions. Using Energy functional, stability of the suggested scheme is achieved. Unique solvability of the difference solutions is proved. Furthermore, the second-order convergence in the discrete H 1 -norm is established. Finally, two numerical experiments are reported to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations, these emergent patterns sometimes appear as local minimisers of a corresponding energy functional. Here we give methods for determining the qualitative structure of local minimum energy states of a broad class of multi-species nonlocal advection–diffusion models, recently proposed for modelling the spatial structure of ecosystems. We show that when each pair of species respond to one another in a symmetric fashion (i.e. via mutual avoidance or mutual attraction, with equal strength), the system admits an energy functional that decreases in time and is bounded below. This suggests that the system will eventually reach a local minimum energy steady state, rather than fluctuating in perpetuity. We leverage this energy functional to develop tools, including a novel application of computational algebraic geometry, for making conjectures about the number and qualitative structure of local minimum energy solutions. These conjectures give a guide as to where to look for numerical steady state solutions, which we verify through numerical analysis. Our technique shows that even with two species, multi-stability with up to four classes of local minimum energy states can emerge. The associated dynamics include spatial sorting via aggregation and repulsion both within and between species. The emerging spatial patterns include a mixture of territory-like segregation as well as narrow spike-type solutions. Overall, our study reveals a general picture of rich multi-stability in systems of moving and interacting species. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following Kirchhoff-type problem: - a + b ∫ R 3 | ∇ u | 2 d x ▵ u + λ V (x) u = g (x , u) + f (x , u) in R 3 , u ∈ H 1 (R 3) , where a, b and λ are real positive parameters. The nonlinearity g (x , u) + f (x , u) may involve a combination of concave and convex terms. By assuming that V represents a potential well with the bottom V - 1 (0) , under some suitable assumptions on f , g ∈ C (R 3 × R , R) , we obtain a positive energy solution u b , λ + via combining the truncation technique and get the asymptotic behavior of u b , λ + as b → 0 and λ → + ∞ . Moreover, we also give the existence of a negative energy solution u b , λ - via Ekeland variational principle. [ABSTRACT FROM AUTHOR]

Brain lesion segmentation can provide useful information for diagnosis and treatment planning. The extracted features are beneficial to the accuracy of brain lesion segmentation. However, due to complex structures of different tissues in different brain modalities, i.e., magnetic resonance imaging (MRI) and computed tomography (CT), the extraction of useful features is a challenging task. In this paper, the effectiveness of four different features, i.e., local intensity, shape, and area to discriminate brain lesion from other normal tissues is explored. Here, the performance of each feature in brain images is analyzed. Next, an energy functional framework integrated with multiple features is implemented. The experiments show that the proposed method can perform well in both real MRI brain tumor and other CT encephalorrhagia segmentation obtained from Quzhou People's hospital. The concrete innovations are as follows: (1) in view of the complexity of brain imaging and the difficulty of identifying lesion region, the proposed method can be applied to the segmentation of more complex brain lesions; (2) multiple features, i.e., local intensity, shape, and area are extracted to construct the proposed energy functional; (3) the proposed model is demonstrated using 32 real MRI images from ten pediatric patients and three different similarity metrics are evaluated. To verify the performance of the proposed algorithm, more than representative 20 images are randomly selected in databases of Quzhou People's hospital for evaluation. The average DICE coefficient, the Jaccard (JAC) distance, the Recall, and Root Mean Square Error (RMSE) are 0.95, 0.90, 0.92, and 0.07, respectively. The proposed method can reach better accuracy performance than the traditional energy functional-based methods and other state-of-the-art brain lesion segmentation methods. [ABSTRACT FROM AUTHOR]

In this paper, we study sufficient conditions for the existence of solutions to a class of damped random impulsive differential equations under Dirichlet boundary value conditions. By using variational method we first obtain the corresponding energy functional. Then the existence of critical points are obtained by using Mountain pass lemma and Minimax principle. Finally we assert the critical point of enery functional is the mild solution of damped random impulsive differential equations.

We give a short survey on plurisubharmonic interpolation, with a focus on the possibility of connecting two given plurisubharmonic functions by plurisubharmonic geodesics.

We describe the 10-dimensional space of Sp (2) -invariant G 2 -structures on the homogeneous 7-sphere S 7 = Sp (2) / Sp (1) as Ω + 3 (S 7) Sp (2) ≃ R + × Gl + (3 , R) . In those terms, we formulate a general Ansatz for G 2 -structures, which realises representatives in each of the 7 possible isometric classes of homogeneous G 2 -structures. Moreover, the well-known nearly parallel round and squashed metrics occur naturally as opposite poles in an S 3 -family, the equator of which is a new S 2 -family of coclosed G 2 -structures satisfying the harmonicity condition div T = 0 . We show general existence of harmonic representatives of G 2 -structures in each isometric class through explicit solutions of the associated flow and describe the qualitative behaviour of the flow. We study the stability of the Dirichlet gradient flow near these critical points, showing explicit examples of degenerate and nondegenerate local maxima and minima, at various regimes of the general Ansatz. Finally, for metrics outside of the Ansatz, we identify families of harmonic G 2 -structures, prove long-time existence of the flow and study the stability properties of some well-chosen examples. [ABSTRACT FROM AUTHOR]

Contraction of actomyosin networks underpins important cellular processes including motility and division. The mechanical origin of actomyosin contraction is not fully-understood. We investigate whether contraction arises on the scale of individual filaments, without needing to invoke network-scale interactions. We derive discrete force-balance and continuum partial differential equations for two symmetric, semi-flexible actin filaments with an attached myosin motor. Assuming the system exists within a homogeneous background material, our method enables computation of the stress tensor, providing a measure of contractility. After deriving the model, we use a combination of asymptotic analysis and numerical solutions to show how F-actin bending facilitates contraction on the scale of two filaments. Rigid filaments exhibit polarity-reversal symmetry as the motor travels from the minus to plus-ends, such that contractile and expansive components cancel. Filament bending induces a geometric asymmetry that brings the filaments closer to parallel as a myosin motor approaches their plus-ends, decreasing the effective spring force opposing motor motion. The reduced spring force enables the motor to move faster close to filament plus-ends, which reduces expansive stress and gives rise to net contraction. Bending-induced geometric asymmetry provides both new understanding of actomyosin contraction mechanics, and a hypothesis that can be tested in experiments. [ABSTRACT FROM AUTHOR]

We consider a Kirchhoff-type equation with critical and supercritical nonlinear terms in a ball. By providing a method of decomposition of energy functional and subtle analysis, we show that every Palais–Smale sequence at a level below a certain energy threshold admits a subsequence that converges strongly to a nontrivial critical point of the variational functional. [ABSTRACT FROM AUTHOR]

In this paper, we propose a user-friendly integral inequality to study the coupled parabolic chemotaxis system with singular sensitivity under the Neumann boundary condition. Under a low diffusion rate, the classical solution of this system is uniformly bounded. Our proof replies on the construction of the energy functional containing ∫Ω|v|4v2 with v>0. It is noteworthy that the inequality used in the paper may be applied to study other chemotaxis systems.

We study a class of reaction–advection–diffusion system ut=∇·(∇u−χ∇vvu)−uv+u−u2+β+B1,x∈Ω,t>0,vt=Δv−v+uv+B2,x∈Ω,t>0,for χ > 0 in a smooth bounded domain Ω⊂ℝn with n ≥ 2. In comparison with original urban crime models (Short et al., 2008), the system introduces the logistic source term u − u2 + β to represent the fierce competition among criminals, which helps to reduce difficulties brought by the nonlinear growth term uv and large advection rate. We prove that, for n ≥ 2, suppose β>0,ifn<4,n4−1,ifn≥4,then the classical solutions (u, v) of the above system are uniformly bounded for any χ > 0. Our result expands χ to be arbitrary positive number. [ABSTRACT FROM AUTHOR]

Active contour model is an extraordinarily valuable technique in image segmentation, which is essential for image analysis and understanding. Active contour model has been widely studied because it delineates closed and smooth contours or surfaces of target objects. However, traditional active contour models underperform on complex natural images. To tackle this problem, we propose a novel active contour model framework, called FeaACM. We introduce the feature energy function into the conventional energy functional to minimize the energy functional to maintain the consistency of the object region and account for different distributions of objects and backgrounds in the feature space. To demonstrate the advantages of our method, we compare our method with the state-of-the-art methods, and show that our method achieves competitive performance. In addition, we utilize AutoEncoder technology to extract the feature of the image verifying the generality of our framework. Extensive and numerous experiments indicate that our method can segment complex natural images effectively. Our code is available at https://github.com/xuepeng1234/FeaACM. • Feature energy was proposed to depict the object in feature space. • A novel variational level set energy functional framework was proposed. • Minimizing the energy functional and maintaining the consistency of the object region simultaneously. [ABSTRACT FROM AUTHOR]

• A new shape of a shell of revolution is presented based on fifth-order polynomial. • Large displacement analysis of fifth-order polynomial–shaped shells is presented. • Continuity requirements are established as the constraint conditions. • Lagrange multipliers associated with constraint equations are used for smooth curve. • Principal curvature in meridional direction on deformed state is presented. The design and construction of submerged complex shells for new applications in offshore structures are increasingly popular. Therefore, the purpose of this study is to present the analytical model and Lagrange multipliers associated with the constraint equation for large displacement analysis of a fifth-order polynomial–shaped shell under hydrostatic pressure for the first time. The shell geometry can be computed using differential geometry with a fifth-order polynomial. The energy functional of the fifth-order polynomial–shaped shell is derived based on the principle of virtual work and written in the appropriate form. The nonlinear static responses of the fifth-order polynomial–shaped shell under hydrostatic pressure can be calculated using the nonlinear finite element method via the fifth-order polynomial shape function. This study develops the model using one-dimensional beam elements divided along the shell radius. To avoid the slope of a meridian curve at the equatorial plane approaching infinity, the shell is divided into two regions defined by different surface parameters. At the junction of two adjacent regions, the continuity requirements are established as the constraint conditions using Lagrange multipliers. The numerical results from the proposed methods are demonstrated and discussed, along with the effects of varied seawater depth, thickness, and elastic modulus on the deformed configuration and principal curvature at the deformed state. The results show that the nonlinear displacement is higher than the linear one in the case of the hydrostatic pressure, whereas the case of the internal pressure has an opposite result. For principal curvatures at the apex, the principal curvatures increase as the seawater depth increases, whereas the principal curvatures decrease when the thickness and elastic modulus increase. [ABSTRACT FROM AUTHOR]

The integration of two vertically crossed re-entrant honeycombs gives rise to a 3D re-entrant honeycomb (3D-RH), which displays intricate three-dimensional auxeticity. To simplify the modeling complexity, this study employs asymptotic analysis of the energy functional stored in the unit cell of the 3D-RH to develop unified constitutive models for 3D structures and panels with multiple length scales. Based on this, an equivalent 3D Cauchy continuum model is established for multi-layer 3D-RH, while a 2D equivalent plate model is developed for sandwich panel with single-layer 3D-RH (SP-3D-RH). The accuracy and effectiveness of these equivalent models are subsequently confirmed through investigations of the X-shaped compressive deformation of multi-layer 3D-RH, as well as the in-plane auxetic deformation and out-of-plane dome-shaped deformation of single-layer 3D-RH. Compared to traditional hexagonal and re-entrant honeycomb sandwich panels, the SP-3D-RH exhibited enhanced equivalent tensile stiffness while effectively mitigating maximum deformation and strain energy under bending and tension conditions. However, due to its relatively low equivalent shear stiffness, the SP-3D-RH exhibited significant deformation and strain energy when subjected to torsional loads, resulting in local stress concentration in the connect region between adjacent facesheets. Parameter analysis shows that the facesheet-to-strut thickness ratio had a substantial impact on the equivalent stiffness and in-plane behavior of the SP-3D-RH, while adjusting the horizontal strut length, strut depth, and re-entrant angle of the 3D-RH can improve the out-of-plane behavior. [Display omitted] • Equivalent models improve efficiency and accuracy in static analysis of 3D-RH. • 3D-EHM captures the X-shaped compressive deformation of multi-layer 3D-RH. • SP-3D-RH shows significant deformation and strain energy under torsional loads. • The facesheet-to-strut thickness ratio affects stiffness and behavior of SP-3D-RH. • 3D-RH in sandwich panel mitigates deformation under tension and bending. [ABSTRACT FROM AUTHOR]

The core layer of accordion honeycomb sandwich panel (accordion HSP) exhibits exceptional affinity for one-dimensional curvature deformations due to its special zero Poisson's ratio effect. This study thoroughly examines its static and dynamic characteristics by decomposing the analysis into unit-cell constitutive modeling and a two-dimensional equivalent-oriented model (2D-EOM) through the variational asymptotic method. The unit-cell constitutive modeling enables determining equivalent stiffness properties for the 2D-EOM. To validate the accuracy and efficiency of the proposed 2D-EOM, its results are compared against those obtained from a detailed 3D finite element model, including in-plane and out-of-plane behaviors of the core layer and sandwich panel, as well as free and random vibration under diverse excitation conditions. The comparison results demonstrate a significant three-fold increase in the equivalent stiffness of the accordion honeycomb in the direction of the added ligaments, as compared to the re-entrant honeycomb. Simultaneously, the acceleration amplitude of the accordion HSP is effectively reduced by 4% due to the involvement of lower high-order frequencies, rendering it exceptionally suited for shockproof meta-structural applications. This equivalent model not only fulfills accuracy requirements but also improves computational efficiency by 15 times, providing an effective approach for preliminary design of honeycomb sandwich panels. • Exceptional affinity for 1D curvature deformations due to ZRP effect of accordion core. • Comprehensive analysis of static and random dynamic characteristics of accordion HSPs. • Enhanced computational efficiency of 2D-EOM while maintaining sufficient accuracy. • Increased stiffness achieved by incorporating ligaments into accordion honeycombs. • Reduced acceleration amplitude due to involvement of lower higher-order frequencies. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper studies the following fractional Kirchhoff equations with steep potential well: 0.1a+b∫ℝN(|(−△)α2u|2)dx(−△)αu+λV(x)u=f(x,u)+μg(x)uq,inℝN,u∈Hα(ℝN),N≥3,where a, b, λ > 0 are parameters, μ > 0, and 0

We equip an arbitrary vector bundle over a Riemannian manifold, endowed with a fiber metric and a compatible connection, with a spherically symmetric metric (cf. [4]), and westudy harmonicity of its sections firstly as smooth maps and then as critical points of the energy functional with variations through smooth sections.We also characterize vertically harmonic sections. Finally, we give some examples of special vector bundles, recovering in some situations some classical harmonicity results. [ABSTRACT FROM AUTHOR]

We prove that every proper n -dimensional length metric space admits an "approximate isometric embedding" into Lorentzian space ℝ 3 n + 6 , 1 . By an "approximate isometric embedding" we mean an embedding which preserves the energy functional on a prescribed set of geodesics connecting a dense set of points. [ABSTRACT FROM AUTHOR]

In this paper, we study the following quasilinear Schrödinger equations −Δu−Δ(|u|2α)|u|2α−2u=ω(x)|u|q−1u,x∈ℝN,where α>12 is a parameter, q>3α−1+α2α, ω(x)∈C(ℝN\{0}) is a positive function. We establish a Liouville type theorem for the class of stable bounded sign‐changing solutions under suitable assumptions on ω(x), q, α and N. [ABSTRACT FROM AUTHOR]

In this paper, we study a couple of NLS equations characterized by mixed cubic and super-linear sub-cubic power laws. Classification as well as existence and uniqueness of the steady state solutions have been investigated. Numerical simulations have been also provided illustrating graphically the theoretical results. Such simulations showed that possible chaotic behaviour seems to occur and needs more investigations. [ABSTRACT FROM AUTHOR]

Variational methods are used to study a model of the deformation of a discontinuous Stieltjes string (a chain of strings held together by springs) located along the segment [0; l]. The model is described by the integro-differential equation pu0 m - (x)+ pu0 m - (0)+ R x 0 ud[Q] = F(x)F(0) with derivatives with respect to the measure m generated by a given strictly increasing function m(x) on the segment [0; l], where the function u(x) determines the deformation of the string, p(x) characterizes the elasticity of the string, the functions Q(x) and F(x) describe the elastic response of the external environment and the external load, respectively. The integral R x 0 ud[Q] is understood in the generalized sense according to Stieltjes. We are looking for solutions u(x) in the class of m-absolutely continuous functions on [0; l], whose derivatives have bounded variation on [0; l]. We assume that one of the boundary conditions is nonlinear and has the form p(l 0)u0 m (l 0)gu(l) 2 N[k;k]u(l); where N[k;k]u(l) denotes the outward normal cone at the point u(l) to the segment [k;k]. This condition arises due to the presence of the limiter [k;k] on the motion of the elastically fixed right end of the string (by a spring with elasticity g) so that ju(l)j = k. In this paper, necessary and sufficient conditions for the minimization of the energy functional of the Stieltjes string system are established, the critical loads at which the contact of the end of the string with the boundary points of the limiter occurs are determined, and the dependence of the solution on the length of the limiter is studied. [ABSTRACT FROM AUTHOR]

The energy functional of the CV and LBF model is single, which makes the curve to get into the local minimum easily during the evolution process, and results inaccurate segmentation of the images with nonuniform grayscale and nonsmooth edges. The proposed algorithm, which is based on local entropy fitting under the constraint of nonconvex regularization term, is used to deal with such problems. In this algorithm, global information and local entropy are fitted to avoid segmentation falling into local optimum, and nonconvex regularization term is imported for constraint to protect edge smoothing. First, global information is used to evolve the approximate contour curve of the target segmentation. Then, a local energy functional with local entropy information is constructed to avoid the segmentation process from falling into a local minimum, and to precisely segment the image. Finally, nonconvex regularization terms are used in the energy functional to protect the smoothness of edge information during image segmentation process. The experimental results clearly indicate that the new algorithm can effectively resist noise, precisely segment images with nonuniform grayscale, and achieve the global optimal. [ABSTRACT FROM AUTHOR]