Monotonic Exponential Decay Research Articles

Initial boundary value problems for a system of parabolic conservation laws arising from chemotaxis in multi-dimensions

We study the qualitative behavior of a system of parabolic conservation laws, derived from a Keller-Segel type chemotaxis model with singular sensitivity, on the unit square or cube subject to various types of boundary conditions. It is shown that for given initial data in $H^3(\Omega)$, under the assumption that only the entropic energy associated with the initial data is small, there exist global-in-time classical solutions to the initial-boundary value problems of the model subject to the Neumann-Stress-free and Dirichlet-Stress-free type boundary conditions; these solutions converge to equilibrium states, determined from initial and/or boundary data, exponentially rapidly as time goes to infinity. In addition, it is shown that the solutions of the fully dissipative model converge to those of the corresponding partially dissipative model as the chemical diffusion rate tends to zero under the Neumann-Stress-free type boundary conditions. Numerical analysis is performed for a discretization of the model with the Dirichlet-Stress-free type boundary conditions, and a monotonic exponential decay to the equilibrium solution (analogous to the continuous case) is proven. Numerical simulations are supplemented to illustrate the exponential decay, test the assumptions of the exponential decay theorem, and to predict boundary layer formation under the Dirichlet-Stress-free type boundary conditions.

Scintillation and optical properties of Ce3+-doped CaGdAl3O7 single crystals

The single crystals of 0, 0.6, 1, 1.6 and 2mol% Ce doped CaGdAl3O7 (Ce:CGAM) were grown by the Floating Zone method, and investigated on photoluminescence (PL) and scintillation properties. In the PL spectra, a broad emission appeared over 380–500nm under 280 and 360nm excitations with the quantum yield of 33.8–38.8%. Under a vacuum ultraviolet excitation (90nm) using a synchrotron source, non-doped CGAM single crystal showed broad emissions over 250–650nm. The PL decay time profiles followed a monotonic exponential decay with a decay time constant of around 33ns. The scintillation spectra were similar to those of PL. All of the samples exhibited a clear photoabsorption peak and Compton edge in the pulse height spectra measured under 137Cs γ-ray irradiation, and the absolute scintillation light yield (LY) was highest for the 2% Ce-doped sample with the value of 3300±300ph/MeV. The scintillation decay profiles were approximated by a third order exponential decay function, and the extracted decay time of Ce3+ emission component was around 36–44ns. Among all the samples, 2%Ce:CGAM single crystal sample showed the best afterglow level as a scintillator under X-ray irradiation.

A three-dimensional map of tidal dissipation over abyssal hills

The breaking of internal tides is believed to provide a large part of the power needed to mix the abyssal ocean and sustain the meridional overturning circulation. Both the fraction of internal tide energy that is dissipated locally and the resulting vertical mixing distribution are crucial for the ocean state, but remain poorly quantified. Here we present a first worldwide estimate of mixing due to internal tides generated at small-scale abyssal hills. Our estimate is based on linear wave theory, a nonlinear parameterization for wave breaking and uses quasi-global small-scale abyssal hill bathymetry, stratification, and tidal data. We show that a large fraction of abyssal-hill generated internal tide energy is locally dissipated over mid-ocean ridges in the Southern Hemisphere. Significant dissipation occurs above ridge crests, and, upon rescaling by the local stratification, follows a monotonic exponential decay with height off the bottom, with a nonuniform decay scale. We however show that a substantial part of the dissipation occurs over the smoother flanks of mid-ocean ridges, and exhibits a middepth maximum due to the interplay of wave amplitude with stratification. We link the three-dimensional map of dissipation to abyssal hills characteristics, ocean stratification, and tidal forcing, and discuss its potential implementation in time-evolving parameterizations for global climate models. Current tidal parameterizations only account for waves generated at large-scale satellite-resolved bathymetry. Our results suggest that the presence of small-scale, mostly unresolved abyssal hills could significantly enhance the spatial inhomogeneity of tidal mixing, particularly above mid-ocean ridges in the Southern Hemisphere.

Electronic conductance via atomic wires: a phase field matching theory approach

A model is presented for the quantum transport of electrons, across finite atomic wire nanojunctions between electric leads, at zero bias limit. In order to derive the appropriate transmission and reflection spectra, familiar in the Landauer-B\"{u}ttiker formalism, we develop the algebraic phase field matching theory (PFMT). In particular, we apply our model calculations to determine the electronic conductance for freely suspended monatomic linear sodium wires (MLNaW) between leads of the same element, and for the diatomic copper-cobalt wires (DLCuCoW) between copper leads on a Cu(111) substrate. Calculations for the MLNaW system confirm the correctness and functionality of our PFMT approach. We present novel transmission spectra for this system, and show that its transport properties exhibit the conductance oscillations for the odd- and even-number wires in agreement with previously reported first-principle results. The numerical calculations for the DLCuCoW wire nanojunctions are motivated by the stability of these systems at low temperatures. Our results for the transmission spectra yield for this system, at its Fermi energy, a monotonic exponential decay of the conductance with increasing wire length of the Cu-Co pairs. This is a cumulative effect which is discussed in detail in the present work, and may prove useful for applications in nanocircuits. Furthermore, our PFMT formalism can be considered as a compact and efficient tool for the study of the electronic quantum transport for a wide range of nanomaterial wire systems. It provides a trade-off in computational efficiency and predictive capability as compared to slower first-principle based methods, and has the potential to treat the conductance properties of more complex molecular nanojunctions.

Enhancement of non-escape probability in open chaotic system due to quantum localization induced by periodic orbits

Abstract We study semiclassically the quantum non-escape probability of a wavepacket initially localized in spatial region Ω , in an open system with fully chaotic classical limit. We show that at time t , the classically diffusive exponential decay is suppressed in leading order of ℏ by the quantum localization due to periodic orbits of period 2 t that are passing through Ω . Each contributing periodic orbit is weighted by the probability density of the initial wave packet along the periodic orbit and a prefactor which counts the stability of the periodic orbit. We argue that the periodic orbits correction will give non-trivial fluctuations superimposed on the monotonic exponential decay at small time and gives arise to anomalous slow decay at large time.

Electrostatic screening in classical Coulomb fluids: exponential or power-law decay or both? An investigation into the effect of dispersion interactions

It is shown that the nature of the non-electrostatic part of the pair interaction potential in classical Coulomb fluids can have a profound influence on the screening behaviour. Two cases are compared: (i) when the non-electrostatic part equals an arbitrary finite-ranged interaction and (ii) when a dispersion r -6 interaction potential is included. A formal analysis is done in exact statistical mechanics, including an investigation of the bridge function. It is found that the Coulombic r -1 and the dispersion r -6 potentials are coupled in a very intricate manner as regards the screening behaviour. The classical one-component plasma (OCP) is a particularly clear example due to its simplicity and is investigated in detail. When the dispersion r -6 potential is turned on, the screened electrostatic potential from a particle goes from a monotonic exponential decay, exp(-κr)/r, to a power-law decay, r -8 , for large r. The pair distribution function acquire, at the same time, an r -10 decay for large r instead of the exponential one. There still remains exponentially decaying contributions to both functions, but these contributions turn oscillatory when the r -6 interaction is switched on. When the Coulomb interaction is turned off but the dispersion r -6 pair potential is kept, the decay of the pair distribution function for large r goes over from the r -10 to an r -6 behaviour, which is the normal one for fluids of electroneutral particles with dispersion interactions. Differences and similarities compared to binary electrolytes are pointed out.

Inviscid long-wave theory for the absolute instability of the rotating-disc boundary layer

This paper is concerned with the absolute instability of the boundary-layer flow produced when an infinite disc rotates in otherwise still fluid. A greater understanding of the mechanisms and properties of the absolute instability is sought through the development of an analytic theory in the inviscid long-wave limit. It is shown that the fundamental basic flow characteristic of the absolute instability is a wall-jet in the radial direction superposed with an asymptotically small cross-flow, which generates a small reverse flow outside the boundary layer in the appropriately resolved basic velocity profile. The absolute instability is produced by a modal coalescence involving the interaction of eight saddle-points of the dispersion relation. An explicit expression for the growth rate has been obtained in terms of basic flow parameters. Most curiously, the pinch-point for absolute instability is shown to become asymptotically close to a branch-cut on the imaginary axis of the complex wavenumber plane, and unstable spatial branches emanating from the pinch-point cross this imaginary axis onto a Riemann sheet of the dispersion relation composed of solutions growing exponentially with distance from the disc. The existence of such modes contradicts the expectation of monotonic exponential decay of disturbances outside a boundary layer.

The decay of pair correlation functions in ionic fluids: A dressed ion theory analysis of Monte Carlo simulations

We analyze the decay of structural correlation functions for 1:1, 1:2, and 2:2 electrolyte solutions obtained from Monte Carlo simulations. It is found that by the use of dressed ion theory and a simple Picard iteration scheme one can extract the leading decay parameters with high accuracy, even from simulations with a rather limited number of ions in the simulation cell. The extraction scheme consists of replacing in a self-consistent manner the tails of the simulated pair distribution functions by analytical expressions evaluated by residue analysis of short-ranged parts of the correlation functions. Numerical results in this work are restricted to primitive model electrolytes where the solvent only enters as a dielectric continuum. The leading decay parameters of the simulated correlation functions are compared to results obtained from the hypernetted chain (HNC) approximation. For 1:1 and 1:2 electrolytes in aqueous solution the simulation results confirm predictions from the HNC approximation. For 2:2 electrolytes the HNC results agree qualitatively with the simulations but deviate quantitatively. To investigate artifacts induced by boundary conditions used in the simulations we analyze correlation functions obtained from simulations in a spherical cell as well as with cubic periodic boundary conditions. The results and method of analysis presented are restricted to electrolyte concentrations at which the leading decay terms of the pair distribution functions exhibit monotonic exponential decay.

Diffusion influenced reversible transfer of electronic excitation energy in liquid solution by long-range interaction

An approach to donor–acceptor kinetics in the presence of diffusion and reversible energy transfer due to microscopic interaction is described. A set of coupled dynamic equations for the reduced distribution functions of reactant molecules in forward and reverse steps is presented on the basis of a hierarchical system of many-body Smoluchowski equations. With a view toward treating long-range dipolar interaction mediated energy transfer kinetics, this formalism is generalized to incorporate unimolecular decay pathways. Numerical calculations of this set of equations for the excited donor decay after a delta pulse show the dependence of the result on acceptor concentration, forward and back transfer distance-dependent rates, donor and acceptor lifetime, and on their diffusive motion. Comparison with the corresponding forward and irreversible reactive dynamics provides detailed insights into the time dependence of flow of electronic excitation in donors and acceptors. The irreversible Smoluchowski limit is only recovered when both the forward and the reverse reactive systems are undergoing fast molecular motion (slow reaction). In the donor–donor case the temporal profile of the excited donor decay and the evolution of ground state donor (that receives energy from the initially excited donor) is presented, along with the total excitation that resides in these two kind of donors. The total excitation in this situation is found to follow a monotonic exponential decay with its characteristic natural lifetime, as expected in a lifetime measurement experiment.

Neuronal nicotinic alpha 7 receptor expressed in Xenopus oocytes presents five putative binding sites for methyllycaconitine.

1. The recently isolated compound methyllycaconitine (MLA) is a plant toxin which is a competitive inhibitor of nicotinic acetylcholine receptors (nAChRs). We found that homomeric alpha 7 receptors display a very high sensitivity to MLA with an IC50 in the picomolar range. 2. The competitive nature of the alpha 7 MLA blockade was reinforced by the observation that this compound has no action on wild-type serotoninergic receptors (5-HT3), whereas it is a powerful antagonist of chimaeric receptors alpha 7-5-HT3. 3. The time course of MLA inhibition of the wild-type (WT) alpha 7 follows a monotonic exponential decay whose time constant is proportional to the MLA concentration and could be described by a bimolecular mechanism with a forward rate constant (k+) of 2.7 x 10(7) S-1 M-1. In contrast, recovery from MLA inhibition displays an S-shaped time course that is incompatible with a simple bimolecular reaction. 4. Given the pentameric nature of the neuronal nicotinic receptors, a linear chain model, including five putative MLA binding sites corresponding to the homomeric nature of alpha 7, is proposed. 5. Both onset and recovery data obtained on the alpha 7 wild-type receptor are adequately described by this model assuming that a single MLA molecule is sufficient to block receptor function. 6. Analysis of MLA blockade and recovery of reconstituted heteromeric alpha 4 beta 2 receptors reveals, as expected, a time course compatible with only two binding sites for the toxin and, thus, further supports the validity of our model.

Asymptotic decay of correlations in liquids and their mixtures

We consider the asymptotic decay of structural correlations in pure fluids, fluid mixtures, and fluids subject to various types of inhomogeneity. For short ranged potentials, both the form and the amplitude of the longest range decay are determined by leading order poles in the complex Fourier transform of the bulk structure factor. Generically, for such potentials, asymptotic decay falls into two classes: (i) controlled by a single simple pole on the imaginary axis (monotonic exponential decay) and (ii) controlled by a conjugate pair of simple poles (exponentially damped oscillatory decay). General expressions are given for the decay length, the amplitude, and [in class (ii)] the wavelength and phase involved. In the case of fluid mixtures, we find that there is only one decay length and (if applicable) one oscillatory wavelength required to specify the asymptotic decay of all the component density profiles and all the partial radial distribution functions gij(r). Moreover, simple amplitude relations link the amplitudes associated with the decay of correlation of individual components. We give explicit results for the case of binary systems, expanding on and partially correcting recent work by Martynov. In addition, numerical results for g(r) for the pure fluid square-well model and for gij(r) for binary hard sphere mixtures are presented in order to illustrate the fact that the asymptotic forms remain remarkably accurate at intermediate range. This is seen to arise because the higher order poles are typically well-separated from the low order ones. We also discuss why the asymptotics of solvation forces for confined fluids and of density profiles of inhomogeneous fluids (embracing wetting phenomena) fall within the same theoretical framework. Finally, we comment on possible modifications to the theory arising from the presence of power-law attractive potentials (dispersion forces).

Dynamics of Bark Beetle Populations: Towards a General Productivity Model 1

The components of productivity (offspring produced per parent) in bark beetle populations are defined as multiplication and survival. Data from the literature are used to formulate simple models relating these components to initial density in infested trees. A simple monotonic exponential decay function is proposed for describing the multiplication component, although data for validation are scarce. A humpbacked function is proposed for the survival component. This model combines 2 equations, one expressing survival as a direct function of attack density, and the other survival as an inverse function of density.

On the Calculation of Autocorrelation Functions of Dynamical Variables

In this paper we develop a formalism for calculating the autocorrelation function of a dynamical variable in terms of a well-defined memory function. Guided by simple physical arguments, an ansatz is adopted for the functional form of the memory function. This ansatz asserts that the memory of dynamical coherence decays exponentially. It is found that: (a) Despite the monotonic exponential decay of the memory function, the autocorrelation function deduced can display negative regions in some circumstances and decay monotonically in other circumstances. (b) The form of the autocorrelation function deduced is identical with that obtained from two other very different analyses, suggesting that the major properties of the function are of general validity. (c) The computed linear momentum autocorrelation function and power spectrum for liquid Ar are in good agreement with the computer experiments of Rahman. (d) The computed dipolar autocorrelation function reproduces all the features of the experimentally determined autocorrelation function, though at present insufficient data are available to provide a quantitative test of the theory. (e) The ansatz used, although obviously not exact, is consistent with the theory of linear regression (Appendix B).