Superlinear Growth Research Articles

On generalized Jacobians in the sense of Clarke for the inverse of a bi‐Lipschitz map and applications in relaxation theory

AbstractRelaxed variational problems in the scalar case involving functions are frequently characterized by the convex envelope of the energy density . For functions with superlinear growth and Lipschitz continuous gradient, a formula for is presented in an open neighborhood of any maximal phase simplex provided that is and strictly convex close to the vertices of the phase simplex. This formula involves a carefully chosen parameterization of which identifies those subsets in in which may be written as a convex combination of a prescribed number of function values.

Unraveling urban dynamics: Scaling laws of human mobility across the cityscape divide

The scaling laws of human mobility are one of the key theories of human geography. They also have important policy implications for urban-rural integration and regional economic growth. Although scaling laws of human mobility have been widely discussed, the allometric growth between urban and rural areas is overlooked. This study aims to fill the gap by investigating scaling laws and power-law distribution across urban and rural areas during urban growth with individual people's trajectory information of 13 million mobile phone users. The analysis identified a turning point at a population of 1.8 million in the Greater Bay Area, where the growth rate of aggregate travel demand stabilizes. The results show that human mobility exhibits segmented allometric growth, with superlinear growth transitioning to sublinear beyond this turning point. The disparities of travel behaviour patterns between urban and rural populations increase as cities grow. These findings would enhance the existing knowledge of the allometric scaling of human mobility.

Why the Fermi paradox may not be well explained by Wong and Bartlett's theory of civilization collapse. A Comment on: 'Asymptotic burnout and homeostatic awakening: a possible solution to the Fermi paradox?' (2022) by Wong and Bartlett.

Wong and Bartlett explain the Fermi paradox by arguing that neither human nor extra-terrestrial civilizations can escape the time window singularity which, they claim, results from the way in which social characteristics of civilizations follow super-linear growth curves of cities. We question if data at the city level necessarily can lead to conclusions at the civilization level. More specifically, we suggest ways in which learnings from research, foresight, diversity and effective future government might act outside of their model to regulate super-linear growth curves of civilizations, and thus substantively increase the likelihood of civilizations progressing towards higher levels of the Kardashev scale. Moreover, we believe their claimed history of the collapse of terrestrial societies used to evidence their model is difficult to justify. Overall, we cast reasonable doubt on the ability of their proposed model to satisfactorily explain the Fermi paradox.

Nucleation-Limited Kinetics of GaAs Nanostructures Grown by Selective Area Epitaxy: Implications for Shape Engineering in Optoelectronics Devices.

The growth kinetics of vertical III-V nanowires (NWs) were clarified long ago. The increasing aspect ratio of NWs results in an increase in the surface area, which, in turn, enhances the material collection. The group III adatom diffusion from the NW sidewalls to the top sustains a superlinear growth regime. In this work, we report on the growth of different GaAs nanostructures by selective area MOVPE on GaAs (111)B substrates. We show that the opening dimensions and geometry qualitatively alter the morphology and height evolution of the structures. We compare the time evolution of vertical GaAs NWs stemming from circular holes and horizontal GaAs nanomembranes (NMs) growing from one-dimensional (1D) rectangular slits on the same substrate. While NW heights grow exponentially with time, NMs surprisingly exhibit sublinear kinetics. The absence of visible atomic steps on the top facets of both NWs and NMs suggests layer-by-layer growth in the mononuclear mode. We interpret these observations within a self-consistent growth model, which links the diffusion flux of Ga adatoms to the position- and shape-dependent nucleation rate on top of NWs and NMs. Specifically, the island nucleation rate is lower on top of the NMs than that on the NWs, resulting in the total diffusion flux being directed from the top facet to the sidewalls. This gives a sublinear height evolution for the NMs. These results open innovative perspectives for shape engineering of III-V nanostructures and new avenues for the design of optoelectronics and photonic devices.

S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms

S-asymptotically $$\omega $$-periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms

Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension

We prove homogenization for viscous Hamilton-Jacobi equations with a Hamiltonian of the form G ( p ) + V ( x , ω ) for a wide class of stationary ergodic random media in one space dimension. The momentum part G(p) of the Hamiltonian is a general (nonconvex) continuous function with superlinear growth at infinity, and the potential V ( x , ω ) is bounded and Lipschitz continuous. The class of random media we consider is defined by an explicit hill and valley condition on the diffusivity-potential pair which is fulfilled as long as the environment is not “rigid”.

The deviation characteristics and influencing factors of urban scaling laws in China: industrial and sectoral perspective

ABSTRACT When facing the complex and enormous system of cities, it is imperative to interpret urban development phenomena in a scientifically rigorous manner. Urban scaling laws describe the logarithmic relationship between the population size of a city and various systemic indicators, providing insights into the reasons behind urban population distribution patterns and scaling characteristics. While research related to urban scaling laws has garnered increasing attention, current studies often focus on revealing the relationships between urban size and economic, social, and infrastructural indicators, neglecting investigations into the relationships between population size and industrial sector indicators. Therefore, this study approaches the topic from the perspective of industries and sectors, employing methods such as ordinary least squares regression and comparative analysis to identify the deviation characteristics of urban scaling laws in China. Additionally, the XGBoost + Shap value modeling method is utilized to discern the factors influencing these deviations. The study findings indicate that from 1988 to 2019, China’s secondary industry scaling index exhibited superlinear growth, while the tertiary industry scaling index demonstrated linear growth, with significant differences observed across various industries. The range of deviation in China’s industry scaling index is relatively large. Among the variables considered, the growth rate of gross domestic product (GDP) exerts the strongest influence on the industry scaling index, followed by urbanization growth rate and urbanization rate. Factors such as population density, per capita national income, and the proportion of secondary industry to GDP also impact industry scaling indices. The research reveals disparities in urban development and suggests responses through urban policy interventions, thereby providing a basis for urban planning and policy formulation.

An extension of the Poincaré–Birkhoff Theorem to systems involving Landesman–Lazer conditions

AbstractWe provide multiplicity results for the periodic problem associated with Hamiltonian systems coupling a system having a Poincaré–Birkhoff twist-type structure with a system presenting some asymmetric nonlinearities, with possible one-sided superlinear growth. We investigate nonresonance, simple resonance and double resonance situations, by implementing some kind of Landesman–Lazer conditions.

Global existence of solutions to some degenerate chemotaxis systems with superlinear growth in cross-diffusion rates and logistic sources

The objective is to investigate the global existence of solutions for degenerate chemotaxis systems with logistic sources in a two-dimensional domain. It is demonstrated that the inclusion of logistic sources can exclude the occurrence of blow-up solutions, even in the presence of superlinear growth in the cross-diffusion rate. Our proof relies on the application of elliptic and parabolic regularity in Orlicz spaces and variational approach.

Positive Radial Symmetric Solutions of Nonlinear Biharmonic Equations in an Annulus

This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵2u=f(u,▵u) on an annular domain Ω in RN with the Navier boundary conditions u|∂Ω=0 and ▵u|∂Ω=0, where f:R+×R−→R+ is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow f(ξ,η) to have superlinear or sublinear growth on ξ,η as |(ξ,η)|→0 and ∞. Our discussion is mainly based on the fixed-point index theory in cones.

Non-autonomous fractional nonlocal evolution equations with superlinear growth nonlinearities

We carry out an analysis of the existence of solutions for a class of nonlinear fractional partial differential equations of parabolic type with nonlocal initial conditions. Sufficient conditions for the solvability of the desired problem are presented by transforming it into an abstract non-autonomous fractional evolution equation, and constructing two families of solution operators based on the Mittag-Leffler function, the Mainardi Wright-type function and the analytic semigroup generated by the closed densely defined operator −A(⋅). The discussions are based on the fractional power theory as well as the Banach fixed point theorem in the interpolation space Xpυ (0⩽υ<1, 1<p<∞).

Elliptic problems with superlinear convection terms

In this manuscript we deal with elliptic equations with superlinear first order terms in divergence form of the following type−div(M(x)∇u)=−div(h(u)E(x))+f(x), where M is a bounded elliptic matrix, the vector field E and the function f belong to suitable Lebesgue spaces, and the function s→h(s) features a superlinear growth at infinity. We provide some existence and non existence results for solutions to the associated Dirichlet problem and a comparison principle.

The Existence and Uniqueness of Radial Solutions for Biharmonic Elliptic Equations in an Annulus

This paper concerns with the existence of radial solutions of the biharmonic elliptic equation ▵2u=f(|x|,u,|∇u|,▵u) in an annular domain Ω={x∈RN:r1&lt;|x|&lt;r2}(N≥2) with the boundary conditions u|∂Ω=0 and ▵u|∂Ω=0, where f:[r1,r2]×R×R+×R→R is continuous. Under certain inequality conditions on f involving the principal eigenvalue λ1 of the Laplace operator −▵ with boundary condition u|∂Ω=0, an existence result and a uniqueness result are obtained. The inequality conditions allow for f(r,ξ,ζ,η) to be a superlinear growth on ξ,ζ,η as |(ξ,ζ,η)|→∞. Our discussion is based on the Leray–Schauder fixed point theorem, spectral theory of linear operators and technique of prior estimates.

Normalized homoclinic solutions of discrete nonlocal double phase problems

The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula: see text], and [Formula: see text]([Formula: see text] or [Formula: see text], [Formula: see text] or [Formula: see text]) is the discrete fractional [Formula: see text]-Laplacian. By variational methods, we discuss the existence of non-negative normalized homoclinic solutions under the conditions that the nonlinear term satisfies sublinear growth or superlinear growth conditions. In particular, we establish the compactness of the associated energy functional of the problem without weights. Our paper is the first time to deal with the existence of normalized solutions for discrete double phase problems.

Electrically driven amplification of terahertz acoustic waves in graphene

In graphene devices, the electronic drift velocity can easily exceed the speed of sound in the material at moderate current biases. Under these conditions, the electronic system can efficiently amplify acoustic phonons, leading to an exponential growth of sound waves in the direction of the carrier flow. Here, we show that such phonon amplification can significantly modify the electrical properties of graphene devices. We observe a superlinear growth of the resistivity in the direction of the carrier flow when the drift velocity exceeds the speed of sound — resulting in a sevenfold increase over a distance of 8 µm. The resistivity growth is observed at carrier densities away from the Dirac point and is enhanced at cryogenic temperatures. We develop a theoretical model for the resistivity growth due to the electrical amplification of acoustic phonons — reaching frequencies up to 2.2 THz — where the wavelength is controlled by gate-tunable transitions across the Fermi surface. These findings provide a route to on-chip high-frequency sound generation and detection in the THz frequency range.

Unstable cores are the source of instability in chemical reaction networks

In biochemical networks, complex dynamical features such as superlinear growth and oscillations are classically considered a consequence of autocatalysis. For the large class of parameter-rich kinetic models, which includes generalized mass action kinetics and Michaelis–Menten kinetics, we show that certain submatrices of the stoichiometric matrix, so-called unstable cores, are sufficient for a reaction network to admit instability and potentially give rise to such complex dynamical behaviour. The determinant of the submatrix distinguishes unstable-positive feedbacks, with a single real-positive eigenvalue, and unstable-negative feedbacks without real-positive eigenvalues. Autocatalytic cores turn out to be exactly the unstable-positive feedbacks that are Metzler matrices. Thus there are sources of dynamical instability in chemical networks that are unrelated to autocatalysis. We use such intuition to design non-autocatalytic biochemical networks with superlinear growth and oscillations.

General laws of funding for scientific citations: how citations change in funded and unfunded research between basic and applied sciences

Abstract Purpose The goal of this study is to analyze the relationship between funded and unfunded papers and their citations in both basic and applied sciences. Design/methodology/approach A power law model analyzes the relationship between research funding and citations of papers using 831,337 documents recorded in the Web of Science database. Findings The original results reveal general characteristics of the diffusion of science in research fields: a) Funded articles receive higher citations compared to unfunded papers in journals; b) Funded articles exhibit a super-linear growth in citations, surpassing the increase seen in unfunded articles. This finding reveals a higher diffusion of scientific knowledge in funded articles. Moreover, c) funded articles in both basic and applied sciences demonstrate a similar expected change in citations, equivalent to about 1.23%, when the number of funded papers increases by 1% in journals. This result suggests, for the first time, that funding effect of scientific research is an invariant driver, irrespective of the nature of the basic or applied sciences. Originality/value This evidence suggests empirical laws of funding for scientific citations that explain the importance of robust funding mechanisms for achieving impactful research outcomes in science and society. These findings here also highlight that funding for scientific research is a critical driving force in supporting citations and the dissemination of scientific knowledge in recorded documents in both basic and applied sciences. Practical implications This comprehensive result provides a holistic view of the relationship between funding and citation performance in science to guide policymakers and R&amp;D managers with science policies by directing funding to research in promoting the scientific development and higher diffusion of results for the progress of human society.

Korn–Maxwell–Sobolev inequalities for general incompatibilities

We establish a family of coercive Korn-type inequalities for generalized incompatible fields in the superlinear growth regime under sharp criteria. This extends and unifies several previously known inequalities that are pivotal to the existence theory for a multitude of models in continuum mechanics in an optimal way. Different from our preceding work [F. Gmeineder, P. Lewintan and P. Neff, Optimal incompatible Korn–Maxwell–Sobolev inequalities in all dimensions, Calc. Var. PDE 62 (2023) 182], where we focused on the case [Formula: see text] and incompatibilities governed by the matrix curl, the case [Formula: see text] considered in this paper gives us access to substantially stronger results from harmonic analysis but conversely deals with more general incompatibilities. Especially, we obtain sharp generalizations of recently proved inequalities by P. Lewintan, S. Müller and P. Neff [Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy, Calc. Var. PDE 60 (2021) 150] in the realm of incompatible Korn-type inequalities with conformally invariant dislocation energy. However, being applicable to higher-order scenarios as well, our approach equally gives the first and sharp inequalities involving Kröner’s incompability tensor inc.

Fractional Evolution Equations with Nonlocal Initial Conditions and Superlinear Growth Nonlinear Terms

Fractional Evolution Equations with Nonlocal Initial Conditions and Superlinear Growth Nonlinear Terms

Mean attractors and invariant measures of locally monotone and generally coercive SPDEs driven by superlinear noise

We study the global solvability, mean attractors and invariant measures for an abstract locally monotone and generally coercive SPDEs driven by infinite-dimensional superlinear noise defined in a dual space of intersection of finitely many Banach spaces. The main feature of this abstract system is that it covers a larger class of fundamental models which are included or not included previously. Under an extended locally monotone variational setting, we establish the global well-posedness, Itô's energy equality and existence of mean random attractors in some high-order Bochner spaces. The existence, uniqueness, support, (high-order and exponential) moment estimates, ergodicity, (pointwise and Wasserstein-type) exponentially mixing and asymptotic stability of invariant measures and evolution systems of measures are discussed for autonomous and nonautonomous stochastic equations. A stopping time technique is used to prove the convergence of solutions in probability in order to overcome the difficulty caused by the local monotonicity and superlinear growth of the coefficients. Our abstract results and unified methods are expected to be applied to various types of SPDEs like 2D Navier-Stokes equations, 2D MHD equations, 2D magnetic Bénard problem, Burgers type equations, 3D Leray α-model, convective Brinkman-Forchheimer equations, fractional (s,p)-Laplacian equations with monotone nonlinearities of polynomial growth of arbitrary order, and others.