This paper concentrates on an interaction scattering problem between the time-harmonic electromagnetic waves and an unbounded periodic elastic medium. The uniqueness results of the interaction problem are established for small frequencies or all frequencies except a discrete set in both the absorbing and non-absorbing medium, and then the existence of solutions is derived by the classical Fredholm alternative. The perfectly matched layer (PML) method is proposed to truncate the unbounded scattering domain to a bounded computational domain. We prove the well-posedness of the solution for the truncated PML problem, where a homogeneous boundary condition is imposed on the outer boundary of the PML. The exponential convergence of the PML method is established in terms of the thickness and parameters of the PML. The proof is based on the PML extension and the exponential decay properties of the modified fundamental solution.

By using the basic principle of the continuous damage mechanics as a reference, together with the statistical strength theory based on the Weibull distribution, a new constitutive model of fractured rock masses for deep underground engineering is proposed. In this model, a new definition of the fracture degree Ft has been proposed for the first time, which can quantitatively describe the fracturing process of a fractured rock mass. Based on the results of laboratory tests and numerical simulations for fractured rock mass specimens, the constitutive model with different fracture degrees are verified. Moreover, the applicability of two yield criteria (the M-C and D-P criteria) for describing the mesoscopic strength of rocks is analyzed. Finally, the effects of the random distribution parameters on the constitutive model are discussed in detail. The results show that the theoretical results agree well with the experimental and numerical results, and the constitutive model with the D-P criterion is better than the model with the M-C criterion.

The present work consisted in developing computational routine for prediction and characterization ignition delay time in shock tube. The work was the development of computational routines to characterize the shock wave parameters the ignition delay times of diesel to validate the experimental tests carried out in shock tube conducted by Santana and compare it with the experimental tests and numerical simulations carried out by others authors available in the literature. A linear regression of the experimental tests conducted by Santana et al [3] with conventional diesel was performed to obtain the Arrhenius equation for numerical simulation of the ignition delay time of diesel under the following conditions: temperatures from 880 to 1300K, pressures 24 bar and equivalence ratio 1. The results show good prediction between experimental and simulations. Were found delay times ranging from 425 to 1890μs. Considering all temperature range, the difference between the experimental and simulated test was approximately 15%, this difference also can be explained by the measurement in the shock tube, that the ignition delay time was calculated by the time difference between the passage of the shock wave by the pressure sensor and the start of the ignition detected by the luminosity detection sensor.

This paper considers relative controllability of leader-follower hybrid delay multi-agent systems under fixed communication topology, where two kinds of state delays are existed and each agent subjects to one of them. Some agents with unidirectional signal flows are assigned as leaders and the others are followers. With neighbor-based protocols adopted, the multi-agent systems are represented as a higher dimensional two-delay system without pairwise matrices permutation. Fundamental solution matrix of the two-delay system is constructed by improving the methods in literature, further solution of the system is obtained. Based on the solution Gramian criterion on relative controllability of the system is established. Whereafter, a sufficient condition on relative controllability of the system is presented. An example is attached to support the work.

In the actual traffic flow, vehicle driving is affected by many random factors. Gaussian white noise is introduced into the optimization velocity model to describe the random behavior, and a stochastic optimization velocity model is proposed. In order to improve the stability of traffic flow, the velocity difference of two successive vehicles ahead is considered, and a velocity difference feedback control model is established by taking the velocity difference between the vehicle and the target two vehicle as the control signal. Then, the stability conditions of stochastic optimization velocity model and feedback control model are obtained by using the moment stability theory. Last, Monte Carlo simulation is used to simulate the traffic. The results show that considering the random factor will reduce the stability of traffic flow, and the feedback control can effectively improve the stability.

Understanding and predicting novel diseases has become very important owing to the huge global health burden. ‎Organiz‎ing and studying mathematical models ‎performs‎ an essential role in predicting the behavior of the ‎disease. ‎In this paper, a new stochastic Susceptible-Infected-Recovered-Death (SIRD) model for spreading epidemic disease is investigated. First, the deterministic SIRD model is considered, and then, by allowing randomness in the recovery and death rates that are not deterministic, the system of nonlinear stochastic differential equations is derived. For the suggested model, the existence and uniqueness of a positive global solution are demonstrated. The parameter estimation is done with the conditional least square estimator for deterministic models and the maximum likelihood estimator for stochastic ones. After that, we investigate a nonadditive state-space model for spreading epidemic disease by considering infected as the hidden process variable. The problem of the hidden process variable from noisy observations is filtered, predicted, and smoothed using a recursive Bayesian technique. For estimating the hidden number of infected variables, closed-form solutions are obtained. Finally, numerical simulations with both simulated and real data are performed to demonstrate the efficiency and accuracy of the current work.

Building on the work in [1], this paper shows how Conformal Geometric Algebra (CGA) can be used to model an arbitrary two-port scattering matrix as a rotation in four dimensional Minkowski space, known as a spinor. This spinor model plays the role of the wave-cascading matrix in conventional microwave network theory. Techniques to translate two-port scattering matrix in and out of spinor form are given. Once the translation is laid out, geometric interpretations are given to the physical properties of reciprocity, loss, and symmetry and some mathe- matical groups are identified. Methods to decompose a network into various sub-networks, are given. An example application of interpolating a 2-port network is provided demonstrating an advantage of the spinor model. Since rotations in four dimensional Minkowski space are Lorentz transformations, this model opens up the field of network theory to physicists familiar with relativity, and vice versa.

The fractional derivatives are not equal for different expressions of the same piecewise function, which caused that the equivalent integral equations of impulsive fractional order system (IFrOS) proposed in existing papers are incorrect. Thus we reconsider two generalized IFrOSs that both have the corresponding impulsive Caputo fractional order system and the corresponding impulsive Riemann-Liouville fractional order system as their special cases, and discover that their equivalent integral equations are two integral equations with some arbitrary constants, which reveal the non-uniqueness of solution of the two generalized IFrOSs. Finally, two numerical examples are offered for explaining the non-uniqueness of solution to the two generalized IFrOSs

The goal of the present paper is to obtain and analyze new exact travelling wave solutions and bifurcation behavior of modified Zakharov-Kuznetsov (mZK) equation with higher order dispersion term. For this purpose, first and second simple methods are used to build soliton solutions of travelling wave solutions. Furthermore, bifurcation behavior of traveling waves including new type of quasiperiodic and multi-periodic traveling wave motions have been examined depending on the physical parameters. Multistability for the nonlinear mZK equation has been investigated depending on fixed values of physical parameters with various initial conditions. The suggested methods for the analytical solutions are powerful and benefical tools to obtain the exact travelling wave solutions of nonlinear evolution equations (NLEEs). Two and three-dimensional plots are also provided to illustrate the new solutions. Bifurcation and multistability behaviors of traveling wave solution of the nonlinear mZK equation with higher order dispersion will add some value in the literature of mathematical and plasma physics.

In this paper, we study the existence and nonexistence of nontrivial solutions to the following critical biharmonic problem with the Steklov boundary conditions Δ2=+Δ+||2**-2 in , =Δ+=0 on , where ,, ∈ , ⊂ N( ≥ 5) is a unit ball, 2** = 2/N-4 denotes the critical Sobolev exponent for the embedding 2() →2** () and is the outer normal derivative of on . Under some assumptions on , and , we prove the existence of nontrivial solutions to the above biharmonic problem by the Mountain pass theorem and show the nonexistence of nontrivial solutions to it by the Pohozaev identity.

A computer program has been created that makes it possible to analyze the features of the spatial distribution of Joule heat in two-phase matrix systems with round inclusions. The program uses the finite element method and is implemented in Fortran code. It was found that at certain points of the two-phase medium, the specific power of the Joule heat is determined. The magnitude of the unevenness of the heat distribution exhibits the ability to level. It was found that the location of the points at which the set parameters for a given structure pm are set depends on the ratio between the conduction of the matrix and the inclusion and the local mutual arrangement of the inclusions. The processes of sintering powder materials using electric heating are considered. It was found that as a result of selective sedimentation, the possibility of the formation of anisotropic structures is turned on. The features of the processes of contact electrical materials based on mixtures of copper and tungsten are discussed. It is assumed that the processes of local heating can initiate the sedimentation of copper particles. In this case, groupings of particles can be formed, oriented along the direction of the heating electric current. The possibility of synthesizing materials similar to composite fiber systems is shown. It is proposed to use computer simulation programs to support heat treatment processes using electric heating.

In this work we consider a generalized Ostrovsky equation depending on two arbitrary functions and we make an in-depth study of this equation. We obtain the Lie symmetries which are admitted by this equation and some exact solutions as a periodic or solitary waves, obtained through ordinary and partial differential equations. Also, by means of the concept of multiplier, we obtain a wide range of conservation laws which preserve properties of the generalized Ostrovsky equation.

A document by JAIRO DE FARIA. Click on the document to view its contents.

In this paper, an valid numerical algorithm is presented to solve variable fractional viscoelastic pipes conveying pulsating fluid in the time domain and analyze dynamically the vortex-induced vibration of the pipes. Firstly, Coimbra variable fractional derivative operators are introduced. Meanwhile, using Hamilton's principle and a nonlinear variable fractional order model, the governing system of equations is established. The unknown functions of the system of equations are approximated with shifted Legendre polynomials. Then, convergence analysis and numerical example investigate the effectiveness and accuracy of the proposed algorithm. Finally, the influences of different parameters on the dynamic response of the viscoelastic pipe are studied. The influencing factors and their ranges of the transient and long-term chaotic states of the pipe are analyzed. In addition, the proposed algorithm shows enormous potentials for solving the dynamics problems of viscoelastic pipes with the variable fractional order models.

A document by Idriss Noureddine Zaouagui. Click on the document to view its contents.

This paper investigates the problem of $H_\infty$ state estimation of delayed recurrent memristive neural networks (DRMNNs) with both continuous-time and discrete-time cases. By utilizing Lyapunov-Krasovskii functional (LKF) and linear matrix inequalities (LMIs), two criterions are provided to guarantee the asymptotically stable of the estimation error systems with a $H_\infty$ performance. The connection weight parameters of DRMNNs are dealed with logical switching signals, which greatly reduces the computational complexity. The given conditions can be easily checked by solving LMIs, the obtained theoretical results are supported demonstrated by two numerical examples.

We study the asymptotic behaviors of the semigroup generated by the linearized Landau operator in the case of the very soft potentials and Coulomb potential. Compared with the hard potentials, Maxwellian molecules and moderately soft potentials, there is no spectral gap for the linearized Landau operator with the very soft and Coulomb potentials. By introducing a new decomposition of the linear Landau collision operator $L$ including an accretive operator and a relatively compact operator, we establish the complete spectrum structure for the linearized Landau operator with the very soft and Coulomb potentials and furthermore derive the time decay estimates of the corresponding semigroup in a weighted velocity space.

In the subcritical energy case, local well-posedness is established in the radial energy space for a class of fractional inhomogeneous Choquard equations. The best constant of a Gagliardo-Nirenberg type inequality is obtained. Moreover, a sharp threshold of global existence versus blow-up dichotomy is obtained for mass super-critical and energy subcritical solutions.