Existence for positive steady states of an eco-epidemiological model

An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered.A system with diffusion under the homogeneous Neumann boundary condition is studied.The existence for a positive solution of the corresponding steady state problem is mainly discussed.First,a prior estimates（positive upper and lower bounds） of the positive steady states of the reaction-diffusion system is given by the maximum principle and the Harnack inequation.Then,the non-existence of non-constant positive steady states by using the energy method is given.Finally,the existence of non-constant positive steady states is obtained by using the topological degree.

POSITIVE STEADY STATES AND DYNAMICS FOR A DIFFUSIVE PREDATOR-PREY SYSTEM WITH A DEGENERACY

In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.

Sawtooth-like oscillations and steady states caused by the m/n=2/1 double tearing mode

The sawtooth-like oscillations resulting from the m/n=2/1 double tearing mode(DTM)are numerically investigated through the three-dimensional,toroidal,nonlinear resistive-MHD code(CLT).We find that the nonlinear evolution of the m/n=2/1 DTM can lead to sawtooth-like oscillations,which are similar to those driven by the kink mode.The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations.With a high perpendicular thermal conductivity,the system quickly evolves into a steady state with m/n=2/1 magnetic islands and helical flow.However,with a low perpendicular thermal conductivity,the system tends to exhibit sawtooth-like oscillations.With a sufficiently high or low heating rate,the system exhibits sawtooth-like oscillations,while with an intermediate heating rate,the system quickly evolves into a steady state.At the steady state,there exist the non-axisymmetric magnetic field and strong radial flow,and both are with helicity of m/n=2/1.Like the steady state with m/n=1/1 radial flow,which is beneficial for preventing the helium ash accumulation in the core,the steady state with m/n=2/1 radial flow might also be a good candidate for the advanced steady state operations in future fusion reactors.We also find that the behaviors of the sawtooth-like oscillations are almost independent of tokamak geometry,which implies that the steady state with saturated m/n=2/1 islands might exist in different tokamaks.

Positive Steady States of a Prey-predator Model with Diffusion and Non-monotone Conversion Rate

In this paper, we study the positive steady states of a prey-predator model with diffusion throughout and a non-monotone conversion rate under the homogeneous Dirichlet boundary condition. We obtain some results of the existence and non-existence of positive steady states. The stability and uniqueness of positive steady states are also discussed.

A Mathematical Model of the Photosynthetic Carbon Metabolism Has Multiple Steady States Under the Same Parameter Conditions

This paper analyzes a mathematical model of the photosynthetic carbon metabolism, which incorporates not only the Calvin-Benson cycle, but also another two important metabolic pathways： starch synthesis and photorespiratory pathway. Theoretically, the paper shows the existence of steady states, stability and instability of the steady states, the effects of CO2 concentration on steady states. Especially, a critical point is found, the system has only one steady state with C02 concentration in the left neighborhood of the critical point, but has two with C02 concentration in the right neighborhood. In addition, the paper also explores the influence of C02 concentration on the efficiency of photosynthesis. These theoretical results not only provide insight to the kinetic behaviors of the photosynthetic carbon metabolism, but also can be used to help improving the efficiency of photosynthesis in plants.

The Local Bifurcation and Stability of Nontrivial Steady States of a Logistic Type of Chemotaxis

Chemotaxis is a type of oriented movement of cells in response to the concentration gradient of chemical substances in their environment. We consider local existence and stability of nontrivial steady states of a logistic type of chemotaxis. We carry out the bifurcation theory to obtain the local existence of the steady state and apply the expansion method on the chemotaxis to investigate the bifurcation direction. Moreover, by applying the bifurcation direction, we obtain the bifurcating steady state is stable when the bifurcation curve turns to right under certain conditions.

Positive Steady States of a Competitor-Competitor-Mutualist Model

In this paper we deal with the positive steady states of a Competitor-Competitor-Mutualist modelwith diffusion and homogeneous Dirichlet boundary conditions.We first give the necessary conditions,and thenestablish the sufficient conditions for the existence of positive steady states.

Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems

The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks,which is an optimization algorithm for finding a local minimum of an objective function.The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions.Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism,we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems.Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states.Moreover,we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications,by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians.Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications.

Non-constant Positive Steady States of the Epidemic Model with Non-monotonic Incidence Rate

In this paper, the positive steady states of the epidemic model with non-monotonic incidence rate are considered. Firstly, it is proved that the unique positive constant steady state is stable for the ODE system and the PDE system. Secondly, a priori estimate of positive steady states is given, and the non-existence of non-constant positive steady states is established by using Poincare inequality and Young inequality. Finally,the existence and bifurcation of non-constant positive steady states are studied by using the degree theory and the global bifurcation theorem.

Steady State Properties of One-Dimensional Non-uniform Granular Gases Subjected to Gaussian White Noise Driving

We present a model of non-uniform granular gases in one-dimensional case, whose granularity distribution has the fractal characteristic. We have studied the nonequilibrium properties of the system by means of Monte Carlo method. When the typical relaxation time T of the Brownian process is greater than the mean collision time To, the energy evolution of the system exponentially decays, with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state in which the velocity distribution strongly deviates from the Gaussian one. Three other aspects have also been studied for the steady state： the visualized change of the particle density, the entropy of the system and the correlations in the velocity of particles. And the results of simulations indicate that the system has strong spatial clustering; Furthermore, the influence of the inelasticity and inhomogeneity on dynamic behaviors have also been extensively investigated, especially the dependence of the entropy and the correlations in the velocity of particles on the restitute coefficient e and the fractal dimension D.

A Stochastic Extension of Macroscopic Stability Criterion of Nonequilibrium Steady State in Chemical Reaction Systems Governed by Master Equation

By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .

Multiple steady state phenomenon in martensitic transformation

Based on the basic facts that the martensitic transformation is a physical phenomenon which occurs in non equilibrium conditions and there exists the feedback mechanism in the martensitic transformation, the dynamical processes of the isothermal and athermal martensitic transformations were analyzed by using nonlinear theory and a bifurcation theory model was established. It is shown that a multiple steady state phenomenon can take place as austenite is cooled, and the transitions of the steady state temperature between the branches of stable steady states can be considered the transformation from austenite to martensite. This model can estimate the starting temperature of the martensitic transformation and explain some experimental features of the martensitic transformation such as the effects of cooling rate, fluctuation and austenitic grain size on the martensitic transformation. [

Rheological behavior of semi-solid 7075 aluminum alloy at steady state

The further application of semi-solid processing lies in the in-depth fundamental study like rheological behavior. In this research, the apparent viscosity of the semi-solid slurry of 7075 alloy was measured using a Couette type viscometer. The effects of solid fraction and shearing rate on the apparent viscosity of this alloy were investigated under different processing conditions. It can be seen that the apparent viscosity increases with an increase in the solid fraction from 10% to 50% （temperature 620 ℃ to 630 ℃） at steady state. When the solid fraction was fixed, the apparent viscosity can be decreased by altering the shearing rate from 61.235 s-1 to 489.88 s-1 at steady state. An empirical equation that shows the effects of solid fraction and shearing rate on the apparent viscosity is fitted： ηα = [0.871 - 0.00849. γ0.74924]. exp（3.7311, fs） . The microstructure of quenched samples was examined to understand the alloy＇s rheological behavior.

Experimental and Finite Element Study of Steady State Micro-cutting Characteristics of Aluminum Alloy (2A12)

This paper studies the micro-cutting characteristics of aluminum alloy (2A12) based on a series of orthogonal experiments and finite element method (FEM) simulations. An energy-based ductile failure law was proposed in the FEM simulation. The simulated cutting forces and chip morphology were compared with experimental results. The simulation result indicates that there is a close relationship between the cutting force and cutting heat. The micro-cutting force decreases as the heat flux vector increases. Both the cutting heat and the micro-cutting force need a finite time to achieve a steady state. It is observed that with the cutting speed of 169.95 m/min and uncut chip thickness of 6 μm, the heat flux vector in the workpiece increases to a stable value after 0.06 ms; meanwhile, the principal cutting force decreases to a steady state correspondingly, i.e., the micro-cutting process achieves the steady state. It is concluded that the steady state micro-cutting simulation can reflect the cutting process accurately.

Realization of minute-long steady-state H-mode discharges on EAST

In the 2016 EAST experimental campaign,a steady-state long-pulse H-mode discharge with an ITER-like tungsten divertor lasting longer than one minute has been obtained using only RF heating and current drive,through an integrated control of the wall conditioning,plasma configuration,divertor heat flux,particle exhaust,impurity management,and effective coupling of multiple RF heating and current drive sources at high injected power.The plasma current（Ip - 0.45 MA） was fully-noninductively driven（Vloop 〈 0.0 V） by a combination of-2.5 MW LHW,-0.4 MW ECH and -0.8 MW ICRF.This result demonstrates the progress of physics and technology studies on EAST,and will benefit the physics basis for steady state operation of ITER and CFETR.

40 Hz Auditory Steady State Response to Linguistic Features of Stimuli during Auditory Hallucinations

The auditory steady state response （ASSR） may reflect activity from different regions of the brain, depending on the modulation frequency used. In general, responses induced by low rates （_〈40 Hz） emanate mostly from central structures of the brain, and responses from high rates （〉80 Hz） emanate mostly from the peripheral auditory nerve or brainstem structures. Besides, it was reported that the gamma band ASSR （30-90 Hz） played an important role in working memory, speech understanding and recognition. This paper investigated the 40 Hz ASSR evoked by modulated speech and reversed speech. The speech was Chinese phrase voice, and the noise-like reversed speech was obtained by temporally reversing the speech. Both auditory stimuli were modulated with a frequency of 40 Hz. Ten healthy subjects and 5 patients with hallucination symptom participated in the experiment. Results showed re- duction in left auditory cortex response when healthy subjects listened to the reversed speech compared with the speech. In contrast, when the patients who experienced auditory hallucinations listened to the reversed speech, the auditory cortex of left hemispheric responded more actively. The ASSR results were consistent with the behavior results of patients. Therefore, the gamma band ASSR is expected to be helpful for rapid and objective diagnosis of hallucination in clinic.

A NEW APPROACH TO THE EQUATIONS FOR THE STEADY STATE CURRENTS AT MICROELECTRODES:EC'PROCESSES(SECOND ORDER REACTION)

With a new approach,the general current expressions of two typical second order catalytic reactions at microelectrodes are obtained.This allows the study of fast chemical reactions and systems where the reactants are present in similar concentrations.

STEADY STATE MOTIONS OF SHALLOW ARCH UNDER PERIODIC FORCE WITH 1:2 INTERNAL RESONANCEON THE PLANE OF PHYSICAL PARAMETERS

The bifurcation dynamics of shallow arch which possesses initial deflection under periodic excitation for the case of 1:2 internal resonance is studied in this paper. The whole parametric plane is divided into several different regions according to lire types of motions; then the distribution of steady state motions of shallow arch on the plane of physical parameters is obtained. Combining with numerical method, the dynamics of the system in different regions, especially in the Hopf bifurcation region, is studied in detail. The rule of the mode interaction and the route to chaos of the system is also analysed at the end.

Modeling and optimization of the cyclic steady state operation of adsorptive reactors

Adsorptive reactors(AR),in which an adsorptive functionality is incorporated into the catalytic reactors,offer enhanced performance over their conventional counterparts due to the effective manipulation of concentration and temperature profiles.The operation of these attractive reactors is,however,inherently unsteady state,complicating the design and operation of such sorption-enhanced processes.In order to capture,comprehend and capitalize upon the rich dynamic texture of adsorptive reactors,it is necessary to employ cyclic steady state algorithms describing the entire reaction-adsorption/desorption cycle.The stability of this cyclic steady state is of great importance for the design and operation of adsorptive reactors.In this paper,the cyclic steady state of previously proposed novel adsorptive reactor designs has been calculated and then optimized to give maximum space–time yields.The results obtained revealed unambiguously that an improvement potential of up to multifold level could be attained under the optimized cyclic steady state conditions.This additional improvement resulted from the reduction of the regeneration time well below the reaction-adsorption time,which means,in turn,more space–time yield.

Evaluation of The Thermal Performance of Multi-Element Doped Graphite under Steady-State High Heat Flux

Multi-element doped graphite, GBST1308 has been developed as a plasma facing material (PFM) for high heat flux components of the HT-7U device. The thermal performance of the material under steady-state (SS) high heat flux was evaluated under actively cooling conditions, the specimens were mechanically joined to copper heat sink with supercarbon sheet as a compliant layer between the interfaces. The experiments have been performed in a facility of ACT (actively cooling test stand) with a 100 kW electron gun in order to test the suitability and the loading limit of such materials. The surface temperature and bulk temperature distribution of the specimens were investigated. The experimental results are very encouraging that when heat flux is not more than 6 MW/m2, the surface temperature of GBST1308 is less than 1000℃, which is the lowest, compared with IG-430U and even with CX-2002U (CFC); The primary results indicate that the mechanically-joined material system by such a proper design as thin tile, super compliant layer, GBST as a PFM and copper-alloy heat sink, can be used as divertor plates for HT-7U in the first phase.