Search results for "equation"

Generalized transport coefficients in a gas with large shear rate

1987

We get a solution of the Bhatnagar-Gross-Krook (BGK) model kinetic equation by means of a perturbative expansion of a temperature gradient to study the transport properties in a gas with large shear rate. The irreversible fluxes are evaluated exactly to first order in the expansion for Maxwell molecules. The transport coefficients obtained are highly nonlinear functions of the shear rate. This dependence on shear rate is analysed and compared with previous results for several transport coefficients. Finally, we have found a solution for a simple model of constant collision frequency for which a large shear rate coexists with an arbitrary temperature gradient.

Activity mediated phase separation: Can we understand phase behavior of the nonequilibrium problem from an equilibrium approach?

2016

We present results for structure and dynamics of mixtures of active and passive particles, from molecular dynamics (MD) simulations and integral equation theory (IET) calculations, for a physically motivated model. The perfectly passive limit of the model corresponds to the phase-separating Asakura-Oosawa model for colloid-polymer mixtures in which, for the present study, the colloids are made self-propelling by introducing activity in accordance with the well known Vicsek model. Such activity facilitates phase separation further, as confirmed by our MD simulations and IET calculations. Depending upon the composition of active and passive particles, the diffusive motion of the active specie…

Spatially limited diffusion coupled with ohmic potential drop and/or slow interfacial exchange: a new method to determine the diffusion time constant…

2004

Abstract We have analyzed chronoamperometric curves, I ( t ), after small-amplitude potential steps Δ E (PITT technique) for the model of linear diffusion of a species inside an electroactive film, taking into account ohmic effects in the external media (solution and electrode) as well as a finite rate of the interfacial exchange. For its short-time interval, t ≪ τ d ( τ d is the diffusion time constant, corresponding to unlimited diffusion from the interface), three approximate analytical expressions have been proposed. One of these represents an interpolation formula between the value of the current at the start of the diffusion process, I (0)=Δ E / R ext (after the end of the EDL chargin…

Liquid–liquid equilibria in the system H3PO4–KCl–H2O–tri-n-butyl phosphate: experiments and modelling

2004

Abstract The liquid–liquid equilibria of the system H3PO4–KCl–H2O–TBP was studied experimentally in the concentration range 0–6 mol/kg. The obtained data were modelled using the Pitzer equation for the aqueous phase and the Sergievskii–Dannus relationship for the organic phase. A fairly good agreement was observed between the model and the experimental data.

Charged particles at fluid interfaces as a probe into structural details of a double layer

2011

Electrostatic interactions between charged, distant colloids in a bulk electrolyte solution do not depend on the inherent structure of ions and a solvent forming a double layer. For charged colloids trapped at an interface between an electrolyte and air this no longer holds; as the electrostatic interactions are mediated via air and the field lines determining the interactions originate at the charged surface, these details come into prominence. Using the Langevin-Poisson-Boltzmann equation we investigate how steric effects and the polarization saturation of a solvent effect the contact potential at the colloid surface and, in consequence, the long range interactions between colloids trappe…

Multireference equation-of-motion coupled cluster theory.

2012

A generalization of the equation-of-motion coupled cluster theory is proposed, which is built upon a multireference parent state. This method is suitable for a number of electronic states of a system that can be described by similar active spaces, i.e., different linear combinations of the same set of active space determinants. One of the suitable states is chosen as the parent state and the dominant dynamical correlation is optimized for this state using an internally contracted multireference coupled cluster ansatz. The remaining correlation and orbital relaxation effects are obtained via an uncontracted diagonalization of the transformed Hamiltonian, Ĥ = e(-T) Ĥe(T), in a compact multire…

1973

In the present paper the connection between an arbitrary polydisperse property and the molecular weight distribution is investigated using exact mathematical methods. On the basis of the superposition principle a general equation is derived which can be applied e.g. to the polydispersity problems connected with the Gel Permeation Chromatography, to the light scattering from dilute solutions of high polymers, or the ultracentrifuge. From this point of view, each of these phenomena is described by help of a linear operator with a special kernel, the analytical or numerical inversion of the operator yielding the molecular weight distribution of the system by help of an uniform algorithm. In de…

Treatment of scalar-relativistic effects on nuclear magnetic shieldings using a spin-free exact-two-component approach.

2013

A cost-effective treatment of scalar-relativistic effects on nuclear magnetic shieldings based on the spin-free exact-two-component theory in its one-electron variant (SFX2C-1e) is presented. The SFX2C-1e scheme gains its computational efficiency, in comparison to the four-component approach, from a focus on spin-free contributions and from the elimination of the small component. For the calculation of nuclear magnetic shieldings, the separation of spin-free and spin-dependent terms in the parent four-component theory is carried out here for the matrix representation of the Dirac equation in terms of a restricted-magnetically balanced gauge-including atomic orbital basis. The resulting spin…

Large Quadratic Hyperpolarizabilities with Donor–Acceptor Polyenes Exhibiting Optimum Bond Length Alternation: Correlation Between Structure and Hype…

1997

Donor-acceptor polyenes of various lengths, and that combine aro- matic electron-donating moieties with powerful heterocyclic electron-withdraw- ing terminal groups, have been synthe- sized and characterized as efficient non- linear optical (NLO) chromophores. Their linear and nonlinear optical proper- ties have been investigated, and variations in these properties have been related to ground-state polarization (dipole p) and structure. In particular, unprecedented quadratic hyperpolarizabilities (p) have been achieved (up to p(0) =I500 x 10-30esu) by reduction of the bond- length alternation (BLA) in the polyenic chain. In each series of homologous com-

Anharmonic vibrational frequency calculations for solvated molecules in the B3LYP Kohn–Sham basis set limit

2012

Abstract The solvent dependence of harmonic and anharmonic vibrational wavenumbers of water, formaldehyde and formamide was studied using the B3LYP method. The results obtained with the hierarchy of Jensen's polarization-consistent basis sets were fitted with two-parameter formula toward the B3LYP Kohn–Sham complete basis set (CBS) limit. Anharmonic corrections have been obtained by a second order perturbation treatment (VPT2) and vibrational configuration interaction (VCI) method. The solvent environment was treated according to the self-consistent reaction field polarizable continuum model (SCRF PCM) approach.