Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures.Comment: 12 pages, 5 figure

Discrete breathers assist energy transfer to ac driven nonlinear chains

One-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in six-order polynomial on-site potentials is considered. Power of the energy source in the form of single ac driven particles is calculated numerically for different amplitudes $A$ and frequencies $\omega$ within the linear phonon band. The results for the on-site potentials with hard and soft nonlinearity types are compared. For the hard-type nonlinearity, it is shown that when the driving frequency is close to (far from) the {\em upper} edge of the phonon band, the power of the energy source normalized to $A^2$ increases (decreases) with increasing $A$. In contrast, for the soft-type nonlinearity, the normalized power of the energy source increases (decreases) with increasing $A$ when the driving frequency is close to (far from) the {\em lower} edge of the phonon band. Our further demonstrations indicate that, in the case of hard (soft) anharmonicity, the chain can support movable discrete breathers (DBs) with frequencies above (below) the phonon band. It is the energy source quasi-periodically emitting moving DBs in the regime with driving frequency close to the DBs frequency, that induces the increase of the power. Therefore, our results here support the mechanism that the moving DBs can assist energy transfer from the ac driven particle to the chain.Comment: 11 pages, 13 figure

Comment on the calculation of forces for multibody interatomic potentials

The system of particles interacting via multibody interatomic potential of general form is considered. Possible variants of partition of the total force acting on a single particle into pair contributions are discussed. Two definitions for the force acting between a pair of particles are compared. The forces coincide only if the particles interact via pair or embedded-atom potentials. However in literature both definitions are used in order to determine Cauchy stress tensor. A simplest example of the linear pure shear of perfect square lattice is analyzed. It is shown that, Hardy's definition for the stress tensor gives different results depending on the radius of localization function. The differences strongly depend on the way of the force definition.Comment: 9 pages, 2 figure

Homoleptic Poly(nitrato) Complexes of Group 14 Stable at Ambient Conditions

Using a novel approach in homoleptic nitrate chemistry, Sn(NO3)62− (3c) as well as the previously unknown hexanitrato complexes Si(NO3)62− (1c), Ge(NO3)62− (2c) were synthesized from the element tetranitrates as salt-like compounds which were isolated and characterized using 1H, 14N, and 29Si NMR and IR spectroscopies, elemental and thermal analyses, and single-crystal XRD. All hexanitrates are moderately air-sensitive at 298 K and possess greater thermal stability toward NO2 elimination than their charge-neutral tetranitrato congeners as solids and in solution. The complexes possess distorted octahedral coordination skeletons and adopt geometries that are highly symmetric (3c) or deformed (1c, 2c) depending on the degree of steric congestion of the ligand sphere. As opposed to the κ2O,O′ coordination mode reported for Sn(NO3)4 previously,1 all nitrato ligands of 3c coordinate in κ1O mode. Six geometric isomers of E(NO3)62− were identified as minima on the PES using DFT calculations at the B3LYP/6-311+G(d,p) level of which two were observed experimentally

Satellite estimates of wide-range suspended sediment concentrations in Changjiang (Yangtze) estuary using MERIS data

The Changjiang (Yangtze) estuarine and coastal waters are characterized by suspended sediments over a wide range of concentrations from 20 to 2,500 mg l-1. Suspended sediment plays important roles in the estuarine and coastal system and environment. Previous algorithms for satellite estimates of suspended sediment concentration (SSC) showed a great limitation in that only low to moderate concentrations (up to 50 mg l-1) could be reliably estimated. In this study, we developed a semi-empirical radiative transfer (SERT) model with physically based empirical coefficients to estimate SSC from MERIS data over turbid waters with a much wider range of SSC. The model was based on the Kubelka–Munk two-stream approximation of radiative transfer theory and calibrated using datasets from in situ measurements and outdoor controlled tank experiments. The results show that the sensitivity and saturation level of remote-sensing reflectance to SSC are dependent on wavelengths and SSC levels. Therefore, the SERT model, coupled with a multi-conditional algorithm scheme adapted to satellite retrieval of wide-range SSC, was proposed. Results suggest that this method is more effective and accurate in the estimation of SSC over turbid water

Indirect Effects in Ecosystems: a Review of Recent Modelling Studies and a Methodological Framework for Comparative Theoretical Analysis

Indirect interrelations between ecosystem processes are often realised after a considerable time lag,and, therefore, are easily overlooked. The understanding of these relationships, however, is indispensable forsustainable development and ecomanagement. Investigation of mechanisms underpinning complex indirectdelayed relationships is greatly aided by advanced mathematical techniques, including correlation, multipleregression and factor analysis, simulation modelling, etc. This paper provides a brief review of the recentrelevant studies. These techniques may be especially useful if used in concert on a range of ecosystems, thusintegrating the information obtained in a comparative theoretical ecosystem analysis (CTEA). Amethodological framework for CTEA is given and possible implications discussed