Initial data for Minkowski stability with arbitrary decay

For the problem of a steady-state flow over a fixed step, in the shallow-water approximation the dependence of the flow regime on the flow direction and the ratio of the fluid depth on the right of the step to the step height are found. The range of admissible values of the fluid flow as a function of the fluid mass flow and the step height is determined. We propose an arbitrary discontinuity decay model for shallow-water equations on a step boundary, which is based on the two-layer representation of fluid flows taking into account the flow peculiarities in the vicinity of a step. A distinctive feature of the suggested model is the separation of a studied flow into two layers in calculating flow quantities near each step, and thus improving approximation of depth-averaged solutions to the initial three-dimensional Euler equations. We are solving the shallow-water equations for one layer, introducing the fictitious lower layer only as an auxiliary structure in setting up the appropriate Riemann problems for the upper layer. Thus, the solution to the problem reduces to an arbitrary discontinuity decay problem for classical shallow-water equations on a plane boundary. The proposed model realizes all analytically possible configurations in the case of presence of the step boundary, qualitatively takes into account the dissipation of translational mechanical energy due to turbulence. A finite-volume numerical method for studying shallow-water flows over the step is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with an advanced consideration of the flow features near the step. The results of computations showing the efficiency of the algorithm developed are discussed.

1-D modelling of radionuclide migration through permeable and fractured rock for arbitrary length decay chains using numerical inversion of Laplace transforms

The report describes an analytic containment building model that is used for calculating the leakage into the environment of each isotope of an arbitrary radioactive decay chain. The model accounts for the source, the buildup, the decay, the cleanup, and the leakage of isotopes that are gas-borne inside the containment building.

In this paper, we consider the nonlinear viscoelastic equation , in a bounded domain with initial conditions and Dirichlet boundary conditions. We prove an arbitrary decay result for a class of kernel function g without setting the function g itself to be of exponential (polynomial) type, which is a necessary condition for the exponential (polynomial) decay of the solution energy for the viscoelastic problem. The key ingredient in the proof is based on the idea of Pata (Q Appl Math 64:499-513, 2006) and the work of Tatar (J Math Phys 52:013502, 2010), with necessary modification imposed by our problem. Mathematical Subject Classification (2010): 35B35, 35B40, 35B60

In this paper, we consider a singular nonlocal viscoelastic problem with a possible damping term . We use the assumptions on the relaxation function due to Tatar (J. Math. Phys. 2011;52:013502) and establish an arbitrary decay result instead of just exponential or polynomial type no matter or . This decay result improves that of Mesloub and Messaoudi (Acta Appl. Math. 2010;110:705–724) where an exponential or polynomial decay result was given for the case .

We study the exponential relaxation of observables propagated with a non-Hermitian transfer matrix, an example being out-of-time-ordered correlations (OTOC) in brick-wall (BW) random quantum circuits. Until a time that scales as the system size, the exponential decay of observables is not usually determined by the second largest eigenvalue of the transfer matrix, as one can naively expect, but it is, in general, slower—this slower decay rate was dubbed “phantom eigenvalue.” Generally, this slower decay is given by the largest value in the pseudospectrum of the transfer matrix; however, we show that the decay rate can be an arbitrary value between the second largest eigenvalue and the largest value in the pseudospectrum. This arbitrary decay can be observed, for example, in the propagation of OTOC in periodic boundary conditions BW circuits. To explore this phenomenon, we study a matrix iteration made from a simple tridiagonal Toeplitz matrix. This setting can be used to propagate OTOC in random circuits with open boundary conditions and to describe a one-dimensional biased random walk with dissipation at the edges. Published by the American Physical Society 2024

In this paper, we consider the following second-order abstract semilinear evolution equation with past history and time delay. Under suitable conditions on initial data, we prove the well-posedness by using the semigroup arguments. The stability result is also established defining a suitable Lyapunov functional for a larger class of kernels. An application is also given.

The effects of a strong standing wave field on the absorption behaviour of a weak probe field are studied. An absorptive medium is assumed to consist of stationary two-level atoms with arbitrary decay and pumping scheme. The spectrum with a resonant saturator does not exhibit emissive behaviour as in the travelling wave cases. With a detuned saturator the spectrum closely resembles the corresponding three-level spectrum. These features are explained from the standing wave induced spatial selectivity and inhomogeneity. The connections to Doppler-broadened spectra are discussed.

It is by now well known that a necessary condition for the exponential (polynomial) decay of the energy of a problem arising in viscoelasticity is that the kernel (which appears in the memory term) itself be of exponential (polynomial) type. By a kernel of exponential (polynomial) type we mean that the product of this kernel with an exponential (polynomial) function is summable. Some researchers have started from this condition to seek other (sufficient) conditions ensuring exponential or polynomial decay of the energy. In this work we generalize these works to an arbitrary decay not necessarily of an exponential or polynomial rate.

This paper is an elaboration of an issue that arose in the paper “Nonuniform Sampling: Bandwidth and Aliasing” [1]. In that paper the single frequency estimation problem was explored using Bayesian probability theory for quadrature data that were sampled nonuniformly and nonsimultaneously. In the process of discussing single frequency estimation, it was shown that the Lomb-Scargle periodogram is the sufficient statistic for single frequency estimation for a stationary sinusoid given real nonuniformly sampled data. Here we demonstrate that the Lomb-Scargle periodogram may be generalized in a straightforward manner to nonuniformly nonsimultaneously sampled quadrature data when the sinusoid has arbitrary decay. This generalized Lomb-Scargle periodogram is the sufficient statistic for single frequency estimation in a wide class of problems ranging from stationary frequency estimation in real uniformly sampled data, to frequency estimation for a single sinusoid having exponential, Gaussian, or arbitrary decay for either real or quadrature data sampled either uniformly or nonuniformly and for quadrature data nonsimultaneously.

Swirling combustion is currently one of the most important engineering problems in physics of combustion. There is a hypothesis on the increase in the combustion efficiency of reacting gas mixtures in combustion chambers with swirling flows, as well as on the increase in the efficiency of fuel combustion devices. In this paper, it is proposed to simulate a swirling flow by taking into account the angular component of the flow velocity. The aim of the study is to determine the effect of the angular component of the flow velocity on the characteristics of the flow and combustion of an air suspension of coal dust in a pipe. The problem is solved in a twodimensional axisymmetric approximation with allowance for a swirling flow. A physical and mathematical model is based on the approaches of the mechanics of multiphase reacting media. A solution method involves the arbitrary discontinuity decay algorithm. The impact of the flow swirl and the size of coal dust particles on the gas temperature distribution along the pipe is determined.

On the complexity of strong approximation of stochastic differential equations with a non-Lipschitz drift coefficient

Narrow-width approximation accuracy

The Office of Civilian Radioactive Waste Management and the Power Reactor and Nuclear Fuel Development Corporation of Japan (PNC) have supported the development of the Analytical Repository Source-Term (AREST) at Pacific Northwest Laboratory. AREST is a computer model developed to evaluate radionuclide release from an underground geologic repository. The AREST code can be used to calculate/estimate the amount and rate of each radionuclide that is released from the engineered barrier system (EBS) of the repository. The EBS is the man-made or disrupted area of the repository. AREST was designed as a system-level models to simulate the behavior of the total repository by combining process-level models for the release from an individual waste package or container. AREST contains primarily analytical models for calculating the release/transport of radionuclides to the lost rock that surrounds each waste package. Analytical models were used because of the small computational overhead that allows all the input parameters to be derived from a statistical distribution. Recently, a one-dimensional numerical model was also incorporated into AREST, to allow for more detailed modeling of the transport process with arbitrary length decay chains. The next step in modeling the EBS, is to develop a model that couples the probabilistic capabilities of AREST with a more detailed process model. This model will need to look at the reactive coupling of the processes that are involved with the release process. Such coupling would include: (1) the dissolution of the waste form, (2) the geochemical modeling of the groundwater, (3) the corrosion of the container overpacking, and (4) the backfill material, just to name a few. Several of these coupled processes are already incorporated in the current version of AREST.

Several concepts of function space controllability and observability of linear retarded systems are re-examined from the point of view of abstract infinite-dimensional systems with state space Rn×L2. It is shown that the controllability of all the eigenmodes, hence feedback stabilizability with an arbitrary exponential decay rate, is implied by a property weaker than the approximate controllability in Rn×L2. Verifiable criteria for this type of controllability and for a related concept of observability are given, along with several examples.