General Energy Decay of Solutions for A Wave Equation with Nonlocal Nonlinear Damping and Source Terms

We consider a wave equation with nonlocal nonlinear damping and source terms.We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique.The main difficult is how to handle with the nonlocal nonlinear damping term.Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso(Evolution Equation and Control Theory,2017(6):437-470)and Narciso(Evolution Equations and Control Theory,2020,9(2):487-508).

Energy Decay for the Elastic Wave Equation with A Local Time-dependent Nonlinear Damping

In this paper, we shall investigate the decay property of the solutions to the initial-boundary value problem for the elastic wave equation with a local time-dependent nonlinear damping. We give some decay rate of the energy when the damping term is effective only in a neighborhood of a suitable subset of the boundary. The results obtained in this paper extend, in particular, the known results for the scalar wave equation.

ENERGY DECAY ESTIMATES FOR AN EULER-BERNOULLI BEAM WITH A TIP MASS

In this paper,we study the energy decay estimates for an Euler-Bernoulli beam with a tip mass,which is clamped at one end and attached a tip mass to the free end.

Global Existence and Energy Decay for a Coupled System of Kirchhoff Type Equations with Damping and Source Terms

This paper deals with the global existence and energy decay of solutions to some coupled system of Kirchhoff type equations with nonlinear dissipative and source terms in a bounded domain. We obtain the global existence by defining the stable set in H0^1 （Ω） × H1 （Ω）, and the energy decay of global solutions is given by applying a lemma of V. Komornik.

DECAY OF ENERGY FOR A DISSIPATIVE ANISOTROPIC ELASTIC SYSTEM

In this article, we study the large-time behavior of energy for a N-dimensional dissipative anisotropic elastic system. By means of multiplicative techniques, energy method, and Zuazua’s estimate technique, we prove the decay property of energy for anisotropic elastic system.

Diagnosis of Kinetic Energy Balance of a Decaying Onland Typhoon

Diagnostic analysis of the balance of kinetic energy (KE) is made for a decaying onland typoon, its external torrential rain area and environment. Results show that, besides low-level frictional dissipation as an energy sink, upper-level horizontal export of KE is another important one for the typhoon. In its decaying KE grows in the external torrential rain area, and the KE production term Gk represents the chief energy source for the torrential rain. The growth of Gk is attributed to the development of the heavy rain and to the heating effect of released latent heat, and the external torrential rain owes its evolution to the exported KE from the strong windbelt in the east of the typhoon and the conversion of synoptic KE into mesoscale perturbation KE. The development of the torrential rain results in the KE feedback to its environment. The KE transfer from the typhoon to the external torrential rain area and then to the environmental region as a mechanism constitutes one of the causes for the rapid disintegration of the tempest.

BEHAVIOR AS t→∞ OF THE SOLUTIONS OF THE LINEAR SYSTEM OF ELASTIC THEORY ON NON－STAR－SHAPED EXTERIOR DOMAINS

The behavior as t→∞ of solutions of the linear system of elastic equations defined on anon-star-tshaped exterior domains in Rn (n≥3) is discussed.It has showed that the local energydecays with arate of t-1+H (0≤H≤1),nonuniformly with respect to the geometrical propertiesof the obstacle.and when n is odd the local energy decays exponentially.For the classical elasticwave,when n=3,the behavior of the solution of the nonhomogeneous system with a right sideterm periodical with respect to time t is discussed.

A Logarithmic Decay of the Energy for the Hyperbolic Equation with Supercritical Damping

We are concerned with the following quasilinear wave equation involving variable sources and supercritical damping:■Generally speaking,when one tries to use the classical multiplier method to analyze tRhe asymptotic behavior of solutions,an inevitable step is to deal with the integralΩ|ut|^(m−2)utudx.A usual technique is to apply Young’s inequality and Sobolev embedding inequality to use the energy function and its derivative to control this integral for the subcritical or critical damping.However,for the supercritical case,the failure of the Sobolev embedding inequality makes the classical method be impossible.To do this,our strategy is to prove the rate of the integral RΩ|u|^(m)dx grows polynomially as a positive power of time variable t and apply the modified multiplier method to obtain the energy functional decays logarithmically.These results improve and extend our previous work[12].Finally,some numerical examples are also given to authenticate our results.

High-Order Fully Discrete Energy Diminishing Evolving Surface Finite Element Methods for a Class of Geometric Curvature Flows

This article concerns the construction of high-order energy-decaying numerical methods for gradient flows of evolving surfaces with curvature-dependent energy functionals.The semidiscrete evolving surface finite element method is derived based on the calculus of variation of the semidiscrete surface energy functional.This makes the semidiscrete problem naturally inherit the energy decay structure.With this property,the semidiscrete problem is furthermore formulated as a gradient flow system of ODEs.The averaged vector-field collocation method is used for time discretization of the ODEs to preserve energy decay at the fully discrete level while achieving high-order accuracy in time.Extensive numerical examples are provided to illustrate the accuracy and energy diminishing property of the proposed method,as well as the effectiveness of the method in capturing singularities in the evolution of closed surfaces.

Alpha decay energies and half-lives for possibly synthesized superheavy elements

We investigate the ground state properties of some superheavy nuclei, which may be synthesized in future experiments. Special emphases are placed on the alpha decay energies and half-lives. The alpha decay energies and half-lives from different theoretical models are compared and discussed comprehensively. Through these calculations and comparisons, the optimal superheavy elements to be synthesized in future experiments are proposed theoretically.

α decay energies and half-lives from a macroscopic-microscopic model

α decay energies of 323 heavy nuclei with Z ≥82 are evaluated with a macroscopic-microscopic model. In this model, the macroscopic part is treated by the continuous medium model and the microscopic part consists of shell and pairing corrections based on the Nilsson potential. α decay half-lives are calculated bY Viola-Seaborg formula. The results of α decay energies and half-lives are compared with experimental values and satisfactory agreement is found. The recoiling effect of the daughter nucleus on α decay half-life is also discussed.

OPTIMAL DECAY RATE OF THE COMPRESSIBLE QUANTUM NAVIER-STOKES EQUATIONS

For quantum fluids governed by the compressible quantum Navier-Stokes equations in R;with viscosity and heat conduction, we prove the optimal L;- L;decay rates for the classical solutions near constant states. The proof is based on the detailed linearized decay estimates by Fourier analysis of the operators, which is drastically different from the case when quantum effects are absent.

Alpha decay half-lives of heavy nuclei within a generalized liquid drop model

Theoretical α-decay half-lives of the heaviest nuclei are calculated using the experimental Qα value. The barriers in the quasi-molecular shape path is determined within a Generalized Liquid Drop Model (GLDM) and the WKB approximation is used. The results are compared with calculations using the DensityDependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulae. The calculations provide consistent estimates for the half-lives of the α decay chains of these superheavy elements. The experimental data stand between the GLDM calculations and VSS ones in the most time.

Behavior of solutions to a Petrovsky equation with damping and variable-exponent sources

This paper deals with the following Petrovsky equation with damping and nonlinear sources:utt+△^(2)u-M(||■u||2^(2))△ut+|ut|^(m(x)-2)ut=|u|^(p(x)-2)u under initial-boundary value conditions,where M(s)=a+b sγis a positive C 1 function with the parameters a>0,b>0,γ≥1,and m(x)and p(x)are given measurable functions.The upper bound of the blow-up time is derived for low initial energy by the differential inequality technique.For m(x)≡2,in particular,the upper bound of the blow-up time is obtained by the combination of Levine's concavity method and some differential inequalities under high initial energy.In addition,we discuss the lower bound of the blow-up time by making full use of the strong damping.Moreover,we present the global existence of solutions and an energy decay estimate by establishing some energy estimates.

Strategies for Improving the Brightness of Aggregation-Induced Emission Materials at Aggregate Level

The brightness of fluorescent agents directly determines the imaging performance as required.Among various fluorophores,small organic species are promising given its exact purity/composition and excellent processibility.However,chromophores with planar geometry may suffer from the undesirable aggregation-caused quenching(ACQ)phenomenon.Encouragingly,luminogens showing aggregation-induced emission(AIE)features are preferable as the aggregates which are the most common used state.In this review,we mainly focus on the strategies employed for boosting the brightness of AIE-active luminogens(AIEgens).From molecule to mor-phology levels,approaches that regulate electronic transition processes of the molecule or the packing extent of aggregates in order to confine molecular motion,reduceπ-πstacking,disrupt fluorophore-water interactions,etc.,are presented.In the end,the current challenges and perspectives are briefly discussed.We anticipate that this review will stimulate new insights and more efforts for the advancement of ultrabright AIEgens.

New Geiger-Nuttall law for cluster radioactivity half-lives

In this study,derived from Balasubramaniam’s formula[Phys.Rev.C 70,017301(2004)]and further considering the effect of the parent nucleus mass,blocking effect,and effect of reduced mass on cluster radioactivity half-lives,we propose a new Geiger-Nuttall law that is model-independent to systematically evaluate the halflives of this process for 16 even-even nuclei and 10 odd-A nuclei.For comparison,a single universal curve for cluster radioactivity andαdecay proposed by Poenaru[Phys.Rev.C 83,014601(2011)],a scaling law proposed by Horoi[J.Phys.G:Nucl.Part.Phys.30,945(2004)],an extension of the Viola-Seaborg formula fromαdecay to cluster radioactivity proposed by Ren et al.[Phys.Rev.C 70,034304(2004)],a new semi-empirical formula for exotic cluster decay proposed by Balasubramaniam et al.[Phys.Rev.C 70,017301(2004)],and a unified formula for the half-lives ofαdecay and cluster radioactivity proposed by Ni et al.[Phys.Rev.C 78,044310(2008)]are also used.The calculated results of our new Geiger-Nuttall law are in good agreement with the experimental half-lives,with the least rms being 0.606,and are better than the compared values.Moreover,we extend this formula to predict the cluster radioactivity half-lives of 51 nuclei whose decay energies are energetically allowed or observed but not yet quantified in NUBASE2020.

Nonlinear Internal Damping of Wave Equations with Variable Coefficients

For wave equations with variable coefficients on regions which are not necessarily smooth, we study the energy decay rate when a nonlinear damping is applied on a suitable subrigion.

Two-proton radioactivity of exotic nuclei beyond proton drip-line

To search for new candidates of the true and simultaneous two-proton(2 p)radioactivity,the 2 p decay energies(Q2 p)are extracted by the Weizs?cker–Skyrme-4(WS4)model,the finite-range droplet model(FRDM),the Koura–Tachibana–Uno–Yamada(KTUY)model and the Hartree–Fock–Bogoliubov mean-field model with the BSk29 Skyrme interaction(HFB29).Then,the 2 p radioactivity half-lives are calculated within the generalized liquid drop model by inputting the four types of Q2 pvalues.By the energy and half-life constraints,it is found that the probable 2 p decay candidates are the nuclei beyond the proton-drip line in the region of Z≤50 based on the WS4 and KTUY mass models.For the FRDM mass model,the probable 2 p decay candidates are found in the region of Z≤44.However,the 2p-decaying candidates are predicted in the region of Z≤58 by the HFB29 mass model.It means that the probable 2 p decay candidates of Z>50 are only predicted by the HFB29 mass model.Finally,the competition between the true 2p radioactivity andα-decay for the nuclei above the N=Z=50 shell closures is discussed.It is shown that~(101)Te,~(111)Ba and~(114)Ce prefer to 2p radioactivity and the dominant decay mode of~(107)Xe and~(116)Ce isα-decay.

Progressive collapse of 2D reinforced concrete structures under sudden column removal

Once a column in building is removed due to gas explosion,vehicle impact,terrorist attack,earthquake or any natural disaster,the loading supported by removed column transfers to neighboring structural elements.If these elements are unable to resist the supplementary loading,they continue to fail,which leads to progressive collapse of building.In this paper,an efficient strategy to model and simulate the progressive collapse of multi-story reinforced concrete structure under sudden column removal is presented.The strategy is subdivided into several connected steps including failure mechanism creation,MBS dynamic analysis and dynamic contact simulation,the latter is solved by using conserving/decaying scheme to handle the stiff nonlinear dynamic equations.The effect of gravity loads,structure-ground contact,and structure-structure contact are accounted for as well.The main novelty in this study consists in the introduction of failure function,and the proper manner to control the mechanism creation of a frame until its total failure.Moreover,this contribution pertains to a very thorough investigation of progressive collapse of the structure under sudden column removal.The proposed methodology is applied to a six-story frame,and many different progressive collapse scenarios are investigated.The results ilustrate the efficiency of the proposed strategy.

Research on some superheavy nuclei

Studies on some superheavy nuclei are performed. The α decay energies are calculated by an improved local binding energy formula, and the α decay half-lives are calculated by the Viola-Seaborg formula. Good agreements between theoretical and experimental results are reached.