Search results for "THERMODYNAMICS"
showing 10 items of 2774 documents
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…
Scenery Flow, Conical Densities, and Rectifiability
2015
We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our main result is a sharp version of the conical density theorem, which we reduce to a question on rectifiability.
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…
Process intensification in a photocatalytic membrane reactor: Analysis of the techniques to integrate reaction and separation
2017
Abstract Different methods to integrate reaction and separation in a membrane reactor are studied in the present work, with the aim being to highlight the pros and cons of the different alternatives and the effects of the intervening parameters. The coupling of the two processes can take place inside a single apparatus or using separate units. If a single apparatus is utilized, the coupling is more direct, but separate units offer higher degrees of freedom for the design with more opportunities to optimize the system without constraints. However, when using separate units, the integration of the two unit operations depends largely on the parameters intervening in the coupling procedure. The…
Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative
2021
Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …
Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential
2015
This note is a continuation of the work \cite{CaoXiangYan2014}. We study the following quasilinear elliptic equations \[ -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\, x\in\mathbb{R}^{N}, \] where $1<p<N,0\leq\mu<\left((N-p)/p\right)^{p}$ and $Q\in L^{\infty}(\R^{N})$. Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
2017
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…
Electron crystallography and non-linear optics
1999
Electron crystallography can be used to obtain specific information about molecular parameters such as the polarisability, dipole moment, and hyperpolarisability. In this, work we show how a combination of quantum mechanics and simulation methods can be used to solve several unknown organic structures and how the calculated molecular parameters can be used to predict the corresponding physical properties of the crystals.
Adsorption of hydrogen isotopes in the zeolite NaX: Experiments and simulations
2017
Abstract Among the different methods to separate hydrogen isotopes one is based on the physisorption at low temperature (below 100 K) where quantum effects induce a particular behavior. In the present work, we study the adsorption of single H 2 and D 2 on the zeolite NaX by combining experiments (manometry) from 30 to 150 K and molecular dynamics simulations at 40 and 77 K. Simulations also include the adsorption analysis for T 2 . Adsorption on NaX membranes is simulated and quantum corrections are introduced by using the well-known Feynman–Hibbs approach into the interaction potentials. Experimental adsorption isotherms are reproduced by using the Toth equation and it is shown that the ad…
The Performance of the Gradient-Like Influence Measure in Generalized Linear Mixed Models
2015
A gradient-like statistic, recently introduced as an influence measure, has been proven to work well in large sample, thanks to its asymptotic properties. In this work, through small-scale simulation schemes, the performance of such a diagnostic measure is further investigated in terms of concordance with the main influence measures used for outlier identification. The simulation studies are performed by using generalized linear mixed models (GLMMs).