Strong Attractor Research Articles

Upper Semicontinuity of Strong Pullback Attractors for Delay Non-autonomous Dynamical Systems and Application to Double Time-delayed 2D MHD Equations

Upper Semicontinuity of Strong Pullback Attractors for Delay Non-autonomous Dynamical Systems and Application to Double Time-delayed 2D MHD Equations

A new 3D full-Stokes calving algorithm within Elmer/Ice (v9.0)

Abstract. A new calving algorithm is developed in the glacier model Elmer/Ice that allows unrestricted calving and terminus advance in 3D. The algorithm uses the meshing software Mmg to implement anisotropic remeshing and allow mesh adaptation at each time step. The development of the algorithm, along with the implementation of the crevasse depth law, produces a new full-Stokes calving model capable of simulating calving and terminus advance across an array of complex geometries. Using a synthetic tidewater glacier geometry, the model is tested to highlight the numerical model parameters that can alter calving when using the crevasse depth law. For a system with no clear attractor at a pinning point, the model time step and mesh resolution are shown to alter the simulated calving. In particular, the vertical mesh resolution has a large impact, increasing calving, as the frontal bending stresses are better resolved. However, when the system has a strong attractor, provided by basal pinning points, numerical model parameters have a limited effect on the terminus evolution. Conversely, transient systems with no clear attractors are highly influenced by the choice of numerical model parameters. The new algorithm is capable of implementing unlimited terminus advance and retreat, as well as unrestricted calving geometries, applying any vertically varying melt distribution to the front for use in conjunction with any calving law or potentially advecting variables downstream. In overcoming previous technical hurdles, the algorithm opens up the opportunity to improve both our understanding of the physical processes and our ability to predict calving.

Iper-luoghi e trame urbane: il ruolo dei centri commerciali nel contesto territoriale lombardo

Abstract Hyper-Places and Urban Fabrics: The Role of Shopping Centers in the Lombardy Territorial Context Moving from a reflection related to urban transformations that have occurred over the years the paper reflects on the generation of new urban spaces – which are configured as strong attractors, connectors, and diffusers – capable of encompassing various individual practices as well as the functions of a society as a whole. Assuming this framework, the contribution focuses on the role of shopping centers – with particular attention to the role assumed by Oriocenter in Lombardy (Italy) – as hyper-places. In fact, since the early 1990s, such structures have undergone profound changes, developing both through an increase in size and through a diversification of commercial attractors, promoting renewed flow trajectories and leading to increasing territorial complexity.

Same, but different: similar states of forest structure in temperate mountain regions of Europe despite different social-ecological forest disturbance regimes

ContextEcosystem services provided by mountain forests are critically linked to forest structure. Social-ecological disturbance regimes (i.e., the rate, frequency, and patch size distribution of disturbances driven by interacting natural and anthropogenic processes) and land use affect forest structure, but their specific impacts are not fully understood.ObjectivesWe examine how differences in disturbance regimes affect patterns of forest structure across three European mountain ranges with similar vegetation types but different land-use histories: the European Alps, the Carpathians, and the Caucasus.MethodsWe related data on horizontal and vertical forest structure, measured by spaceborne lidar (GEDI), with Landsat-derived information on forest disturbances (1986–2020) and topographic, climatic, and anthropogenic predictors.ResultsWe found similar social-ecological disturbance regimes in the Alps and Carpathians (average annual disturbance rates of 0.34% and 0.39%, respectively, and median patch size < 0.5 ha), yet much lower disturbance rates and patch sizes in the Caucasus (0.08% yr−1 and < 0.2 ha). Despite different disturbance regimes, we found similar patterns of forest structure. Two alternative states emerged consistently across all mountain ranges: a tall and closed-canopy state in 74–80% of forests and a low and open-canopy state (< 50% canopy cover) in the rest. While forest structure responded consistently to abiotic drivers such as topography and climate, its association with anthropogenic pressures differed between mountain ranges. Stand-replacing disturbances played an important role in the Carpathians, while forest structure in the Caucasus was related to proximity to settlements, reflecting local forest use.ConclusionsDifferent social-ecological contexts in mountain regions can produce markedly different forest disturbance regimes. Despite these differences, similar states of forest structures emerge, suggesting strong attractors of structure in temperate mountain forests.

Strong solutions and attractor dimension for 2D NSE with dynamic boundary conditions

We consider incompressible Navier–Stokes equations in a bounded 2D domain, complete with the so-called dynamic slip boundary conditions. Assuming that the data are regular, we show that weak solutions are strong. As an application, we provide an explicit upper bound of the fractal dimension of the global attractor in terms of the physical parameters. These estimates comply with analogous results in the case of Dirichlet boundary condition.

Comment on: Criteria for Strong and Weak Random Attractors

AbstractIn the article ’Criteria for Strong and Weak Random Attractors’ necessary and sufficient conditions for strong attractors and weak attractors are studied. In this note we correct two of its theorems on strong attractors.

Complete regularity and strong attractor for the structurally damped wave equation with subcritical-critical nonlinearities on $ \mathbb{R}^{N} $

Complete regularity and strong attractor for the structurally damped wave equation with subcritical-critical nonlinearities on $ \mathbb{R}^{N} $

Stability of strong attractors for the extensible beam equation with gentle dissipation

The paper investigates the stability of the strong global and exponential attractors for the extensible beam equation with gentle dissipation: utt−βM(‖∇u‖2)Δu+Δ2u+(−Δ)2αut+f(u)=g(x), where the perturbed parameter α∈(0,1/2] is a dissipative index and β∈[0,1] is an extensibility parameter. We show that when the nonlinearity f(u) is of the optimally subcritical growth depending on α: 1≤p<pα:=N+8α(N−4)+, (i) the strong (H,H2)-global attractors obtained in [15] for this model are upper semicontinuous with respect to α in H2-topology and with respect to β in stronger V4×V2+α1-topology, with α1∈(0,α), respectively; (ii) for any fixed β∈[0,1] and α0∈(0,1/2], the related dynamical system (Sα(t),H) has a family of strong (H,H2)-exponential attractors Eexpα which are continuous with respect to α at α0 in H2-topology; (iii) for any fixed α∈(0,1/2], the related dynamical system (Sβ(t),H) has a family of strong (H,V4×V2+2α1)-exponential attractors Eexpβ which are Hölder continuous with respect to β at any point β0∈[0,1] in V4×V2+2α1-topology. All these strong global and exponential attractors are also the standard global and exponential attractors of optimal regularity. The method used here allows to obtain the stability of the strong attractors with respect to the perturbed parameters in strong topology instead of only standard energy topology.

Geographical immobility and local ancestral ties: a study of three generations of natives in Finland

ABSTRACT Research concerning internal migration has increasingly recognized family members outside the household as important factors for mobility decisions. Older generations and familiar environments constitute strong attractors thanks to location-specific capital and exchange of multigenerational support. Less is known about geographical immobility across generations. Wee study immobility patterns across three generations of native Finns by examining population register data that span over five decades. We analyse how geographical immobility in terms of a person’s place of residence at age 35 vs age 14 relates to the place of birth of their parents and grandparents. In this regard, Finland offers a highly useful case study because of its two main ethnolinguistic groups, Finnish and Swedish speakers, which are characterized by historically different mobility patterns and geographical concentrations. We find that geographical immobility relates strongly to local ancestral ties, that geographical immobility is much more common among Swedish than Finnish speakers, that the association between local ancestral ties and geographical immobility is stronger for Swedish than for Finnish speakers, and that it differs across geographical areas with different ethnolinguistic profiles. In terms of effect sizes, local ancestral ties have a large role in immobility behaviour, equally important as many socioeconomic and demographic factors.

Design, analysis, circuit implementation, and synchronization of a new chaotic system with application to information encryption

The practical applications of chaotic systems are gaining more dimensions every day. In this paper, a new 3D chaotic system is presented with three nonlinear terms and unique strong chaotic behavior. For the initial evaluation of the behavior of the innovative chaotic system, analyses related to equilibrium points, sensitivity, stability, Lyapunov exponent, and bifurcation have been carried out, and its strong attractor manner has been well shown. The practical realization of the designed system is shown by its circuit implementation through the use of electronic elements and Kirchhoff’s laws. To show the performance of the innovative system in practical applications, first a synchronization technique inspired by non-linear and active approaches has been designed, and then by using the innovative chaotic system in the masking technique, a new information encryption method has been derived. The results obtained from the masking based on the innovative chaotic system and the designed synchronization technique show the high functionality of the derivative encryption method.

Spatiotemporal bias of the human gaze toward hierarchical visual features during natural scene viewing

The human gaze is directed at various locations from moment to moment in acquiring information necessary to recognize the external environment at the fine resolution of foveal vision. Previous studies showed that the human gaze is attracted to particular locations in the visual field at a particular time, but it remains unclear what visual features produce such spatiotemporal bias. In this study, we used a deep convolutional neural network model to extract hierarchical visual features from natural scene images and evaluated how much the human gaze is attracted to the visual features in space and time. Eye movement measurement and visual feature analysis using the deep convolutional neural network model showed that the gaze was more strongly attracted to spatial locations containing higher-order visual features than to locations containing lower-order visual features or to locations predicted by conventional saliency. Analysis of the time course of gaze attraction revealed that the bias to higher-order visual features was prominent within a short period after the beginning of observation of the natural scene images. These results demonstrate that higher-order visual features are a strong gaze attractor in both space and time, suggesting that the human visual system uses foveal vision resources to extract information from higher-order visual features with higher spatiotemporal priority.

Stability of strong exponential attractors for the Kirchhoff wave model with structural nonlinear damping

This paper investigates the stability of strong exponential attractors with respect to dissipative index θ∈[1/2,1) for the Kirchhoff wave model with structural nonlinear damping: utt−ϕ(‖∇u‖2)Δu+σ(‖∇u‖2)(−Δ)θut+f(u)=g(x). It proves that for each θ0∈[1/2,1), there exists a family of strong bi-space exponential attractors, which are also the standard exponential attractors of optimal regularity and are Hölder continuous at the point θ0 in the topology of the strong solution space provided that the nonlinearity f(u) is of the optimal subcritical growth. The method used here allows to overcome the difficulties in literatures before to get the Lipschitz continuity and quasi-stability of the evolution semigroup Sθ(t) to obtain the desired result.

Strongly compact strong trajectory attractors for evolutionary systems and their applications

We show that for any fixed accuracy and time length T, a finite number of T-time length pieces of the complete trajectories on the global attractor are capable of uniformly approximating all trajectories within the accuracy in the natural strong metric after sufficiently large time when the observed dissipative system is asymptotically compact. Moreover, we obtain the strong equicontinuity of all the complete trajectories on the global attractor. These results follow by proving the existence of a strongly compact strong trajectory attractor. The notion of a trajectory attractor was previously constructed for a family of auxiliary systems including the originally considered one without uniqueness. Recently, Cheskidov and the author developed a new framework called evolutionary system, with which a (weak) trajectory attractor can be actually defined for the original system. In this paper, the theory of trajectory attractors is further developed in the natural strong metric for our purpose. We then apply it to both the 2D and the 3D Navier–Stokes equations and a general nonautonomous reaction–diffusion system.

Strong attractors and their stability for the structurally damped Kirchhoff wave equation with supercritical nonlinearity

This paper investigates the complete regularity of the weak solutions, the existence of the strong ‐global and exponential attractors, and their stability on dissipative index for the structurally damped Kirchhoff wave equation: , together with the Dirichlet boundary condition, where the perturbed parameter is called a dissipative index, is energy space, and is strong solution space. We show that when the nonlinearity is of supercritical growth: , (i) the weak solutions of the model are just the strong ones; (ii) the global and exponential attractors of the related dynamical system obtained in literature before are exactly the strong ‐ones, and the family of strong ‐global attractors is upper semicontinuous on in ‐topology; (iii) for each , has a family of strong ‐exponential attractors , which is Hölder continuous at in ‐topology. The method developed here allows establishing the above‐mentioned results, which breakthrough the restriction on this topic in literature before.

Complete regularity and strong attractor for the strongly damped wave equation with critical nonlinearities on $$\mathbb {R}^{3}$$

Complete regularity and strong attractor for the strongly damped wave equation with critical nonlinearities on $$\mathbb {R}^{3}$$

Pullback trajectory attractor for nonautonomous wave equations

We consider the dynamical behavior for nonautonomous wave equations without uniqueness. The existence of both pullback weak and strong trajectories is proved. In order to obtain pullback strong trajectory attractor, we use the measure of noncompactness to verify evolutionary process is pullback strong asymptotically compact. The external force is not needed to be translation bounded.

Strong attractors for the strongly damped wave equations on time-dependent spaces

We examine the long-term behavior of strong solutions for the wave equation $ \varepsilon(t)u_{tt}-\Delta u_{t}-\Delta u+f(u) = g(x) $ and obtain the time-dependent attractor in $ \mathcal{H}_{t}^{1} = [H^{2}(\Omega)\cap H_{0}^{1}(\Omega)]\times H_{0}^{1}(\Omega) $. Moreover, the attractor is bounded in $ [H^{2}(\Omega)\cap H_{0}^{1}(\Omega)]\times[H^{2}(\Omega)\cap H_{0}^{1}(\Omega)] $.

Entropy estimates for uniform attractors of 2D Navier–Stokes equations with weakly normal measures

This paper aims at the long-time behavior of non-autonomous 2D Navier–Stokes equations with a class of external forces which are [Formula: see text]-valued measures in time. We first establish the well-posedness of solutions as well as the existence of a strong uniform attractor, and then pay the main attention on the estimation of [Formula: see text]-entropy for such uniform attractor in the standard energy phase space.

Dynamic analysis of porosity dependent functionally graded sigmoid piezoelectric (FGSP) plate

This paper analyzes the vibration behaviour of the functionally graded sigmoid piezoelectric (FGSP) plate subjected to electrical and mechanical loading of a porous and non-porous plate. The sigmoid law is used for the variations of material properties along with the direction of thickness with different porosity types, i.e. even and uneven types. The plate incorporates the geometrical nonlinearity with von Kármán strains and First-order shear deformation theory (FSDT) based displacement field. For getting the nonlinear governing equation from Hamilton's principle or energy principle and higher-order numerical formulation with nine nodded isoperimetric elements and the six degrees of freedom per node. The perfect FGSP plate shows multi-periodic excitation with two strong attractors for SSSS boundary conditions, while quasi-periodic responses and 3-T periodic responses are observed for CCCC and CFFF boundary conditions. For evenly distributed porous SSSS FGSP square plate, the center displacement increases with an increase of the porosity from 0.2 to 0.4, while for un-evenly distributed porous center displacement reduces with a rise of the porous exponent from 0.2 to 0.4. The current analysis outcomes can be used for perfect and porous functionally graded piezoelectric smart structure applications under different electromechanical loading environments.

Strong attractors for weakly damped quintic wave equation in bounded domains

In this paper, we study the longtime dynamics for the weakly damped wave equation with quintic non-linearity in a bounded smooth domain of R3. Based on the Strichartz estimates for the case of bounded domains, we establish the existence of a strong global attractor in the phase space H2(Ω)∩H01(Ω)×H01(Ω). Moreover, the finite fractal dimension of the attractor is also shown with the help of the quasi-stable estimation.