Search results for "equation"
showing 10 items of 4219 documents
Theoretical study on hydrogen storage capacity of expanded h-BN systems
2017
In this work, the hydrogen storage capacity of the expanded hexagonal Boron Nitride (eh-BN) systems has been presented. We have employed a new equation of state (EOS) for hydrogen gas to figure out the hydrogen density distribution profiles in the eh-BN systems. In this regard, the environmental conditions (i.e., temperature and pressure) are considered in the prediction procedure using DFT single point calculations. The eh-BN systems with different layer spacings are studied by PBE method with consideration of the long range dispersion corrections. On account of the in-plane polar bonds, a series of adsorption positions are considered. Additionally, the adsorption energy and hydrogen densi…
Resonant activation in polymer translocation: new insights into the escape dynamics of molecules driven by an oscillating field
2010
The translocation of molecules across cellular membranes or through synthetic nanopores is strongly affected by thermal fluctuations. In this work we study how the dynamics of a polymer in a noisy environment changes when the translocation process is driven by an oscillating electric field. An improved version of the Rouse model for a flexible polymer has been adopted to mimic the molecular dynamics, by taking into account the harmonic interactions between adjacent monomers and the excluded-volume effect by introducing a Lennard–Jones potential between all beads. A bending recoil torque has also been included in our model. The polymer dynamics is simulated in a two-dimensional domain by num…
Guidelines for the assessment of the rate law of slurry photocatalytic reactions
2017
Abstract The assessment of the rate law of slurry photocatalytic reactions appears to be a hard task, mainly because in this type of reactions the average rate of reaction, which is experimentally observed in a real reactor, could be very different from the “true” (intrinsic) rate of reaction, which cannot be measured directly. In the present work, it is shown how a proper mathematical model allows the utilization of the differential and/or the integral methods of kinetic analysis. The mathematical model must take into account not only the momentum and the mass balances, but also the radiative transfer equation. However, the discrimination among different proposed kinetic laws remains diffi…
Integro-differential equation modelling heat transfer in conducting, radiating and semitransparent materials
1998
In this work we analyse a model for radiative heat transfer in materials that are conductive, grey and semitransparent. Such materials are for example glass, silicon, water and several gases. The most important feature of the model is the non-local interaction due to exchange of radiation. This, together with non-linearity arising from the well-known Stefan-Boltzmann law, makes the resulting heat equation non-monotone. By analysing the terms related to heat radiation we prove that the operator defining the problem is pseudomonotone. Hence, we can prove the existence of weak solution in the cases where coercivity can be obtained. In the general case, we prove the solvability of the system us…
A thermodynamically consistent cohesive-frictional interface model for mixed mode delamination
2016
Abstract A new interface constitutive model based on damage mechanics and frictional plasticity is presented. The model is thermodynamically consistent, it is able to accurately reproduce arbitrary mixed mode debonding conditions and it is proved that the separation work is always bounded between the fracture energy in mode I and the fracture energy in mode II. Analytical results are given for proportional loading paths and for two non-proportional loading paths, confirming the correct behavior of the model for complex loading histories. Numerical and analytical solutions are compared for three classical delamination tests and frictional effects on 4ENF are also considered.
Flying Laser Spot Thermography technique for the NDE of Fibre Metal Laminates disbonds
2017
Abstract The present work investigates the features of an active Infrared-NDT Thermography technique derived from a Flying Laser Spot set-up for the analysis of interlaminar disbonds in layered structures in general and Fibre Metal Laminates in particular. The presented technique uses a laser-spot heat source, which moves at a constant speed, raster scanning the object surface. Interlaminar defects parallel to the surfaces act as barriers towards through-the-thickness heat diffusion. This produces some modifications over the surface thermal field which are well identified in the Standard Deviation calculated over a Reference Area following the heat source. The mechanisms leading to such def…
Determination of the apparent activation energy of dielectric relaxation phenomena by means of the representation of ε” as a function of T at constan…
1984
Abstract The main purpose of this work is to justify the use of the positions of the maxima of e” versus T curves when calculating the apparent activation energy in secondary dielectric relaxations or in the relaxation associated with the glass transition. To exemplify this, phenomenological models as well as experimental results for methacrylic polymers are discussed.
Two relaxation times and thermal nonlinear waves along wires with lateral heat exchange
2021
Abstract We propose a model for studying several nonlinear waves for heat transport along a cylindrical system with lateral non-linear heat transfer to the environment. We consider relaxational equations, each with its own relaxation time, for longitudinal heat transfer and for lateral heat transfer across the wall. We consider two kinds of nonlinear lateral heat transport: radiative heat transport, and flux-limited heat transport. This work generalizes our previous studies in which the relaxation time for the lateral heat transfer was considered equal to that of the longitudinal heat flux. We explore the influence of both relaxation times on the propagation speed of linear and nonlinear wa…
Zero-range model of traffic flow.
2005
A multi--cluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is directly mapped to the mathematically well-studied zero-range process. Knowledge of the asymptotic behaviour of the transition rates for large clusters allows us to apply an established criterion for phase separation in one-dimensional driven systems. The distribution over cluster sizes in our zero-range model is given by a one--step master equation in one dimension. It provides an approximate mean--field dynamics, which, however, leads to the exact stationary s…
Characteristics of the polymer transport in ratchet systems
2010
Molecules with complex internal structure in time-dependent periodic potentials are studied by using short Rubinstein-Duke model polymers as an example. We extend our earlier work on transport in stochastically varying potentials to cover also deterministic potential switching mechanisms, energetic efficiency and non-uniform charge distributions. We also use currents in the non-equilibrium steady state to identify the dominating mechanisms that lead to polymer transportation and analyze the evolution of the macroscopic state (e.g., total and head-to-head lengths) of the polymers. Several numerical methods are used to solve the master equations and nonlinear optimization problems. The domina…