GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

Dialectical Thermodynamics’Solution to the Conceptual Imbroglio That Is the Reversible Path

According to the second law of thermodynamics, as currently understood, any given transit of a system along the reversible path proceeds with a total entropy change equal to zero. The fact that this condition is also the identifier of thermodynamic equilibrium, makes each and every point along the reversible path a state of equilibrium, and the reversible path, as expressed by a noted thermodynamic author, “a dense succession of equilibrium states”. The difficulties with these notions are plural. The fact, for example, that systems need to be forced out of equilibrium via the expenditure of work, would make any spontaneous reversible process a consumer of work, this in opposition to common thermodynamic wisdom that makes spontaneous reversible processes the most efficient transformers of work-producing-potential into actual work. The solution to this and other related impasses is provided by Dialectical Thermodynamics via its previously proved notion assigning a negative entropy change to the energy upgrading process represented by the transformation of heat into work. The said solution is here exemplified with the ideal-gas phase isomerization of butane into isobutane.

Dynamics and Exact Solutions of (1 + 1)-Dimensional Generalized Boussinesq Equation with Time-Space Dispersion Term

We study exact solutions to (1 + 1)-dimensional generalized Boussinesq equation with time-space dispersion term by making use of improved sub-equation method, and analyse the dynamical behavior and exact solutions of the sub-equation after constructing the nonlinear transformation and constraint conditions. Accordingly, we obtain twenty families of exact solutions such as analytical and singular solitons and singular periodic waves. In addition, we discuss the impact of system parameters on wave propagation.

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.

Effect of two-step solid solution on microstructure andδphase precipitation of Inconel 718 alloy

Inconel 718 is the most popular nickel-based superalloy and is extensively used in aerospace,automotive,and energy indus-tries owing to its extraordinary thermomechanical properties.The effects of different two-step solid solution treatments on microstructure andδphase precipitation of Inconel 718 alloy were studied,and the transformation mechanism fromγ″metastable phase toδphase was clarified.The precipitates were statistically analyzed by X-ray diffractometry.The results show that theδphase content firstly increased,and then decreased with the temperature of the second-step solid solution.The changes in microstructure andδphase were studied by scanning electron microscopy and transmission electron microscopy.An intragranularδphase formed in Inconel 718 alloy at the second-[100]_(δ)[011]γ step solid solution temperature of 925℃,and its orientation relationship withγmatrix was determined as//and(010)_(δ)//(111)γ.Furthermore,the Vickers hardness of different heat treatment samples was measured,and the sample treated by second-step solid solution at 1010℃ reached the maximum hardness of HV 446.84.

Diversity of Rogue Wave Solutions to the (1+1)-Dimensional Boussinesq Equation

A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 but also has a relationship with the other parameters c0, α, β.

PDE Standardization Analysis and Solution of TypicalMechanics Problems

A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.

THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE

In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.

Solution approximations for a mathematical model of relativistic electrons with beta derivative

The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta derivative.For this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are used.While applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact solution.The advantage of this procedure is that discretization or normalization is not required.By applying the mETF,the exact solutions are obtained.Also,by applying the HAM semi-analytical results for the considered equation are acquired.In HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution series.Also,comparative graphical representations are given to show the effectiveness,reliability of the methods.The results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta derivative.This study can bring a new perspective for studies on fractional differential equations.On the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and etc.which involves fractional differentiation.Briefly the results may cause a new insight who studies on relativistic electron modelling.

Analytic Solutions for Hindered Rotation Quantum Problem

Normalizable analytic solutions of the quantum rotor problem with divergent potential are presented here as solution of the Schrödinger equation. These solutions, unknown to the literature, represent a mathematical advance in the description of physical phenomena described by the second derivative operator associated with a divergent interaction potential and, being analytical, guarantee the optimal interpretation of such phenomena.

Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

Positon and hybrid solutions for the(2+1)-dimensional complex modified Korteweg-de Vries equations

Solving nonlinear partial differential equations have attracted intensive attention in the past few decades. In this paper, the Darboux transformation method is used to derive several positon and hybrid solutions for the(2+1)-dimensional complex modified Korteweg–de Vries equations. Based on the zero seed solution, the positon solution and the hybrid solutions of positon and soliton are constructed. The composition of positons is studied, showing that multi-positons of(2+1)-dimensional equations are decomposed into multi-solitons as well as the(1+1)-dimensions. Moreover, the interactions between positon and soliton are analyzed. In addition, the hybrid solutions of b-positon and breather are obtained using the plane wave seed solution, and their evolutions with time are discussed.

Malargüe Site Remediation:A Successful Solution for Uranium Mill Tailings

Comisión Nacional de Energía Atómica (CNEA) has the responsibility for restoring uranium mining facilities once the operations have finished.CNEA,within its Environmental Program and in compliance with its legal responsibilities,decides to implement a restoration project for all sites related to the mining and processing of uranium ores.The Malargüe Site is located within the Province of Mendoza in the city of Malargüe.It is the first site to successfully complete its remediation.The activities consist of relocation of tailings to an engineering repository.The tailings management(encapsulation) and rehabilitation of the area was finished in June 2017.The remediation alternative for the ore tailings was selected after conducting comparative studies and submitted the project to the society for consideration.The objective of the encapsulation of the mineral tails is to isolate them from the environment,also proceeding with the decontamination and rehabilitation of the area (landscaping,post-closure monitoring and 20 years monitoring period).Encapsulation consisted of the construction of a containment cell for the mine tailings,to isolate them and prevent pollutants from entering the environment through the transfer routes.To clean the impacted areas,the soil was removed,it was incorporated into the encapsulation,and the filling was carried out with natural soils from the area.Remediation prevents radon transfer to the environment,as ^(222)Ra is an alpha emitter with a half-life of four days,which produces its own radioactive progeny.Radon progeny are solids,and when a ^(222)Ra nucleus emits an alpha particle into the air,the resulting ^(218)Po nucleus,momentarily electrically charged,adheres to any dust particle.Remediation prevents the discharge into the air containing radon and also containing dust particles charged with intensely radioactive radon progeny.The tasks mentioned make it possible to decrease radon emanation,reduce radiological risks to the public and prevent the entry of rainwater into the system.In addition,the containment system prevents the discharge of contaminated liquids into the environment,avoiding contamination of the groundwater.All these activities are according to the concepts of sustainability.

GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

On entire solutions of some Fermat type differential-difference equations

On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].

Enhancing Cybersecurity through Cloud Computing Solutions in the United States

This study investigates how cybersecurity can be enhanced through cloud computing solutions in the United States. The motive for this study is due to the rampant loss of data, breaches, and unauthorized access of internet criminals in the United States. The study adopted a survey research design, collecting data from 890 cloud professionals with relevant knowledge of cybersecurity and cloud computing. A machine learning approach was adopted, specifically a random forest classifier, an ensemble, and a decision tree model. Out of the features in the data, ten important features were selected using random forest feature importance, which helps to achieve the objective of the study. The study’s purpose is to enable organizations to develop suitable techniques to prevent cybercrime using random forest predictions as they relate to cloud services in the United States. The effectiveness of the models used is evaluated by utilizing validation matrices that include recall values, accuracy, and precision, in addition to F1 scores and confusion matrices. Based on evaluation scores (accuracy, precision, recall, and F1 scores) of 81.9%, 82.6%, and 82.1%, the results demonstrated the effectiveness of the random forest model. It showed the importance of machine learning algorithms in preventing cybercrime and boosting security in the cloud environment. It recommends that other machine learning models be adopted to see how to improve cybersecurity through cloud computing.

Effect of inorganic salt impurities on seeded precipitation of silica hydrate from sodium silicate solution

To clarify the precipitation of silica hydrate from the real desilication solutions of aluminosilicate solid wastes by adding seeds and improve integrated waste utilization,the seeded precipitation was studied using synthesized sodium silicate solution containing different inorganic salt impurities.The results show that sodium chloride,sodium sulfate,sodium carbonate,or calcium chloride can change the siloxy group structure.The number of high-polymeric siloxy groups decreases with increasing sodium chloride or sodium sulfate concentration,which is detrimental to seeded precipitation.Calcium chloride favors the polymerization of silicate ions,and even the chain groups precipitate with the precipitation of high-polymeric sheet and cage-like siloxy groups.The introduced sodium cations in sodium carbonate render a more open network structure of high-polymeric siloxy groups,although the carbonate ions favor the polymerization of siloxy groups.No matter how the four impurities affect the siloxy group structure,the precipitates are always amorphous opal-A silica hydrate.