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Free and forced damped vibrations of a Duffing equation with cubic nonlinearities is considered. The damping, nonlinearity and external excitation parameters are assumed to vary slowly in time. Using the Method of Multiple Scales, a perturbation technique, the amplitude and phase modulation equations are derived in its most general case. First, the free vibration case is treated. Decaying, built-up and harmonically varying functions are taken to model the slow variations of the parameters in time. The amplitude and phase modulation equations can be integrated to obtain closed form solutions in general for free vibrations. For the forced vibrations, a resort to the numerical techniques is required for the integration of the amplitude and phase modulation equations. It is shown that slow variations on the coefficients may lead to substantial changes in the dynamics of the problem. [ABSTRACT FROM AUTHOR]

The customers' impatience and its effect plays a major role in the economy of a country. It directly affects the sales of products and profit of a trading company. So, it is very important to study various impatient behaviors of customers and to analyze different strategies to hold such impatient customers. This situation is modeled mathematically in this research work along with working vacation and reserved idle time of server, balking and re-service of customers. This paper studies the transient analysis of an M/M/1 queueing model with variant impatient behavior, balking, re-service, reserved idle time and working vacation. Whenever the system becomes empty, the server resumes working vacation. When he is coming back from the working vacation and finding the empty system, he stays idle for a fixed time period known as reserved idle time and waits for an arrival. If an arrival occurs before the completion of reserved idle time, the server starts a busy period. Otherwise, he resumes another working vacation after the completion of reserved idle time. During working vacation, the arriving customers may either join or balk the queue. The customers waiting in the queue for service, during working vacation period, become impatient. But, the customer who is receiving the service in the slow service rate, does not become impatient. After each service, the customer may demand for immediate re-service. The transient system size probabilities for the proposed model are derived using generating function and continued fraction. The time-dependent mean and variance of system size are also obtained. Finally, numerical illustrations are provided to visualize the impact of various system parameters. [ABSTRACT FROM AUTHOR]

In this paper we study the time differential dual-phase-lag model of heat conduction incorporating the microstructural interaction effect in the fast-transient process of heat transport. We analyze the influence of the delay times upon some qualitative properties of the solutions of the initial boundary value problems associated to such a model. Thus, the uniqueness results are established under the assumption that the conductivity tensor is positive definite and the delay times τ q and τ T vary in the set {0 ≤ τ q ≤ 2 τ T } ∪ {0 < 2 τ T < τ q }. For the continuous dependence problem we establish two different estimates. The first one is obtained for the delay times with 0 ≤ τ q ≤ 2 τ T , which agrees with the thermodynamic restrictions on the model in concern, and the solutions are stable. The second estimate is established for the delay times with 0 < 2 τ T < τ q and it allows the solutions to have an exponential growth in time. The spatial behavior of the transient solutions and the steady-state vibrations is also addressed. For the transient solutions we establish a theorem of influence domain, under the assumption that the delay times are in {0 < τ q ≤ 2 τ T } ∪ {0 < 2 τ T < τ q }. While for the amplitude of the harmonic vibrations we obtain an exponential decay estimate of Saint–Venant type, provided the frequency of vibration is lower than a critical value and without any restrictions upon the delay times. [ABSTRACT FROM AUTHOR]

In the paper by Ham et al. (2014), the method of finite spheres enriched for transient wave propagation problems was used and a monotonic convergence of the calculated solutions with decreasing time step size was seen. This is an important property for practical analyses and different from what is seen in traditional finite element solutions. In this paper we explicitly show and study this characteristic through a dispersion analysis of the solutions calculated by the method of finite spheres using an implicit time integration method, the Bathe method. Another important property identified is that in uniform spatial discretizations for the problems solved, the calculated solution accuracy is almost independent of the solution direction considered. Numerical solutions of some wave propagation problems are given to demonstrate these attributes and show that with the schemes discussed very accurate response predictions can be obtained. [ABSTRACT FROM AUTHOR]

Abstract: Previous research into the neutral theory of biodiversity has focused mainly on equilibrium solutions rather than time-dependent solutions. Understanding the time-dependent solutions is essential for applying neutral theory to ecosystems in which time-dependent processes, such as succession and invasion, are driving the dynamics. Time-dependent solutions also facilitate tests against data that are stronger than those based on static equilibrium patterns. Here I investigate the time-dependent solutions of the classic spatially implicit neutral model, in which a small local community is coupled to a much larger metacommunity through immigration. I present explicit general formulas for the eigenvalues, left eigenvectors and right eigenvectors of the models’s transition matrix. The time-dependent solutions can then be expressed in terms of these eigenvalues and eigenvectors. Some of these results are translated directly from existing results for the classic Moran model of population genetics (the Moran model is equivalent to the spatially implicit neutral model after a reparameterization); others of the results are new. I demonstrate that the asymptotic time-dependent solution corresponding to just these first two eigenvectors can be a good approximation to the full time-dependent solution. I also demonstrate the feasibility of a partial eigendecomposition of the transition matrix, which facilitates direct application of the results to a biologically relevant example in which a newly invading species is initially present in the metacommunity but absent from the local community. [Copyright &y& Elsevier]

In the present paper we consider the linear theory of thermoelasticity of type III for anisotropic and inhomogeneous materials as developed by Green and Naghdi (1992, 1995). We consider the general initial-boundary value problems associated with the theory in concern and then we identify some mild constitutive hypotheses that lead to appropriate energetic measures of solutions. On this basis we are able to prove some new uniqueness and continuous data dependence theorems. When the boundary surface is maintained at zero thermal displacement, we are able to obtain uniqueness and continuous data dependence results by using only the positiveness of the density mass, the positive definiteness of the elasticity tensor and the positive definiteness of the heat conductivity tensor, without any sign defined assumption upon the specific heat. These results are established by means of new techniques which are essentially different from those previously used for the classical theory of thermoelasticity. [ABSTRACT FROM AUTHOR]

In the industrial film casting process with the two-stage cascade (velocity and tension controlled) loop, various aspects of nonlinear dynamics and chaotic motion have been investigated solving simple 1-D viscoelastic model. Most of the extensional deformation processes exhibit sustained-periodic oscillations or stable limit cycles of state variables (called draw resonance instability) beyond the critical onset, even if they are conventionally controlled systems. Besides such well-known instability, some intriguing nonlinear dynamic phenomena such as period-doubling and eventual chaotic motion of film thickness and width could be observed when a disturbance is imposed in the second tension-controlled system. In other words, the bifurcation mode is dramatically changed by a sinusoidal disturbance under the combined velocity-tension control condition in contrast to only constant take-up velocity condition inducing a supercritical Hopf bifurcation of draw resonance. [ABSTRACT FROM AUTHOR]

Transient solutions for M/M/c queues are important for staffing call centers, police stations, hospitals and similar institutions. In this paper we show how to find transient solutions for M/M/c queues with finite buffers by using eigenvalues and eigenvectors. To find the eigenvalues, we create a system of difference equations where the coefficients depend on a parameter x. These difference equations allow us to search for all eigenvalues by changing x. To facilitate the search, we use Sturm sequences for locating the eigenvalues. We also show that the resulting method is numerically stable. [ABSTRACT FROM AUTHOR]

In the transient solutions of fiber spinning and film casting process dynamics accompanied by spinline flow-induced crystallization was investigated incorporating flow-induced crystallization kinetics into the mathematical model of the system and then devised proper numerical schemes to generate the temporal pictures of the system. It turns out that the difficulty obtaining the transient solutions of the processes accompanied by flow-induced crystallization lies in, among these, the extremely high sensitivity of the spinline velocity towards the fluid stress level. The transient solutions thus obtained will be used for developing optimal strategies to enhance the stability and productivity of the processes. [ABSTRACT FROM AUTHOR]

In this paper we study the spatial behaviour for a large class of isotropic and homogeneous porous thermoelastic materials for which the constitutive coefficients are supposed to satisfy some relaxed positive definiteness conditions. By using some appropriate measures, we are able to establish results describing the spatial behaviour of transient and steady-state solutions in these enlarged classes of thermoelastic porous materials. [ABSTRACT FROM AUTHOR]

Abstract: The existence of optimal cooling conditions with respect to process stability has been experimentally found in film blowing, in a sharp contrast to other extensional deformation processes such as fiber spinning and film casting where maximum, not optimal, cooling always unequivocally enhances process stability. The same simulation model of film blowing of Hyun et al. [J.C. Hyun, H. Kim, J.S. Lee, H.-S. Song, H.W. Jung, Transient solutions of the dynamics in film blowing processes, J. Non-Newtonian Fluid Mech., 121 (2004) 157–162] proven quite accurate in portraying the transient dynamic behavior of the film blowing as compared with experimental data, has been used in this study to carry out a linear stability analysis, which then clearly confirms the experimentally found optimal cooling conditions. These optimal cooling conditions in film blowing stemming from the multiplicity of steady states of the process thus make the strategies for stabilization and optimization of the process quite a challenging task in both industry and academia because of their common relevance to the important process productivity issue. [Copyright &y& Elsevier]

Abstract: The transient solutions of the fiber spinning process when flow-induced crystallization occurs on the spinline have not been reported yet in the literature. By contrast, the steady state behavior is well understood and has been simulated by many researchers, as has the transient behavior with no crystallization on the spinline. In this study, this particular issue has been investigated in the low-speed spinning case where no necklike deformation occurs on the spinline, incorporating flow-induced crystallization into the mathematical model of the system and then devising proper numerical schemes to produce temporal pictures of fiber spinning process. It turns out that the difficulty in obtaining transient solution for fiber spinning when it is accompanied by flow-induced crystallization lies in the extreme sensitivity of the spinline velocity toward the fluid stress level. This parameter plays a key role in finding the spinneret stress level for the numerical marching scheme employed in obtaining the solutions of the governing equations. This is in sharp contrast to the case of no crystallization on the spinline where the profiles of spinline variables are almost insensitive to the spinneret stress level, thus allowing previous researchers to obtain transient solutions with little difficulty. In addition to the successful transient solutions of fiber spinning dynamics with flow-induced crystallization reported in the present study, it is also shown that the destabilizing effect of flow-induced crystallization in low speed spinning process is confirmed by a linear stability analysis. [Copyright &y& Elsevier]

This paper is concerned with a dynamic linear theory for binary mixtures of thermoelastic bodies. We study the spatial behavior for some classes of isotropic and homogeneous thermoelastic mixture materials for which the constitutive coefficients are supposed to satisfy various mild positive definiteness conditions. By introducing some appropriate measures, we are able to establish results describing the spatial behavior of the transient solutions in bounded as well as unbounded bodies. [ABSTRACT FROM AUTHOR]

In this paper two solution methods to the MAP(t)/PH(t)/1/K queueing model are introduced, one based on the Backwards Euler Method and the other on the Uniformization Method. Both methods use finite-differencing with a discretized, adaptive time-mesh to obtain time-dependent values for the entire state probability vector. From this vector, most performance parameters such as expected waiting time and expected number in the system can be computed. Also presented is a technique to compute the entire waiting (sojourn) time distribution as a function of transient time. With these two solution methods one can examine any transient associated with the MAP(t)/PH(t)/1/K model including time-varying arrival and/or service patterns. Four test cases are used to demonstrate the effectiveness of these methods. Results from these cases indicate that both methods provide fast and accurate solutions to a wide range of transient scenarios. [ABSTRACT FROM AUTHOR]

The computational problem of transient solutions for denumerable state Markov Processes (MP's) has been solved by Hsu and Yuan [12], who derived an efficient algorithm with uniform error. However, when the state space of an MP is of two or more dimensions, even for computational methods dealing with stationary solutions, only the case where one of the dimensions is infinite and all the others are finite has been studied. In this paper, we study transient solutions for multidimensional denumerable state MP's and give an algorithm with uniform error. Some numerical results are presented. [ABSTRACT FROM AUTHOR]