Search results for " solution"
showing 10 items of 3084 documents
The influence of the solvent's mass on the location of the dividing surface for a model Hamiltonian
2019
The Transition State dividing surface is a key concept, not only for the precise calculation of the rate constant of a reaction, but also for the proper prediction of product ratios. The correct location of this surface is defined by the requirement that reactive trajectories do not recross it. In the case of reactions in solution the solvent plays an important role in the location of the dividing surface. In this paper we show with the aid of a model Hamiltonian that the effective mass of the solvent can dramatically change the location of the dividing surface. Keywords: Dynamical systems, Dividing surface, Reactions in solution, 2019 MSC: 00-01, 99-00
Strong etching formulation (time and rate) for PADC with deep depth bulk etch rate study
2021
Abstract Aqueous NaOH with ethanol (strong) etchant is widely used. It shortens etching time effectively compared to normal etching conditions (6.25N NaOH at 70 °C). Two equations have been proposed to calculate the etching time with NaOH molarity and ethanol volume. Another two empirical equations were introduced for estimating the bulk etch rates of PADC etched in strong etchant. Up to now, there were no such equations available in the literature that can predict etching time and V b of PADC with etchant molarity and ethanol volumes. The proposed equations were compared to fundamental V b models stemming from literature. Fast etching enables the follow-up of bulk etch rate variation versu…
Beyond the Vegard's law: solid mixing excess volume and thermodynamic potentials prediction, from end-members
2020
Abstract A method has been developed, herein presented, to model binary solid solutions' volume, enthalpy and Gibbs energy using the energy state functions, E ( V , S ) , of the end-members only. The E ( V , S ) s are expanded around an unknown mixing volume, V Mix , and the fundamental equilibrium equation − ( ∂ E / ∂ V ) S = P is used to determine V Mix . V Mix allows us to model enthalpy, straightforwardly. The same argument holds using Helmholtz energy, F ( V , T ) , in place of E ( V , S ) , and the equilibrium equation becomes − ( ∂ F / ∂ V ) T = P . One can readily determine the Gibbs free energy, too. The method presented remarkably simplifies computing of solid mixings' thermodynam…
Dynamical behaviour of an XX central spin model through Bethe ansatz techniques
2009
Following the Bethe ansazt procedure the exact dynamics of an XX central spin model is revealed. Particular initial conditions are analyzed and the consequent time evolution is compared with the exact solution obtained by solving the time-dependent Schrudinger equation. The interest towards spin systems and in particular central spin systems, is motivated by the recent developments in more applicative contexts.
Pair and triple correlations in theA+B→Bdiffusion-controlled reaction
1994
An exact solution for the one-dimensional kinetics of the diffusion-controlled reaction A+B\ensuremath{\rightarrow}B is obtained by means of the three-particle correlation functions. Because of a lattice discreteness each site could be occupied by a single particle only which leads to the so-called ``bus effect'': Recombination of any particle A is defined by a spatial configuration of two nearest particles B only surrounding A from its left and right. This results in the unusual algebraic decay law, n(t)\ensuremath{\propto}${\mathit{t}}^{\mathrm{\ensuremath{-}}1}$, which asymptotically (as t\ensuremath{\rightarrow}\ensuremath{\infty}) does not depend on the trap B concentration.
One pendulum to run them all
2013
The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented.
An intrinsic characterization of the Schwarzschild metric
1998
An intrinsic algorithm that exclusively involves conditions on the metric tensor and its differential concomitants is presented to identify every type-D static vacuum solution. In particular, the necessary and sufficient explicit and intrinsic conditions are given for a Lorentzian metric to be the Schwarzschild solution.
Cosmological solutions in theD=5 Einstein-Maxwell theory coupled to matter
1991
We study the Einstein-Maxwell theory in five dimensions coupled to matter in two distinct ways. In the first we reduce the Lagrangian to an effective four-dimension one and then we couple it to matter; in the second, we introduce matter directly in the original five-dimensional theory. In both cases we use a non trivial configuration for the Maxwell potential. We find non singular solutions which present a repulsive gravitational phase. When this phase is absent, the initial singularity is unavoidable.
Wormholes supported by hybrid metric-Palatini gravity
2012
Recently, a modified theory of gravity was presented, which consists of the superposition of the metric Einstein-Hilbert Lagrangian with an $f(\cal R)$ term constructed \`{a} la Palatini. The theory possesses extremely interesting features such as predicting the existence of a long-range scalar field, that explains the late-time cosmic acceleration and passes the local tests, even in the presence of a light scalar field. In this brief report, we consider the possibility that wormholes are supported by this hybrid metric-Palatini gravitational theory. We present here the general conditions for wormhole solutions according to the null energy conditions at the throat and find specific examples…
Rotating black holes in Eddington-inspired Born-Infeld gravity: an exact solution
2020
We find an exact, rotating charged black hole solution within Eddington-inspired Born-Infeld gravity. To this end we employ a recently developed correspondence or {\it mapping} between modified gravity models built as scalars out of contractions of the metric with the Ricci tensor, and formulated in metric-affine spaces (Ricci-Based Gravity theories) and General Relativity. This way, starting from the Kerr-Newman solution, we show that this mapping bring us the axisymmetric solutions of Eddington-inspired Born-Infeld gravity coupled to a certain model of non-linear electrodynamics. We discuss the most relevant physical features of the solutions obtained this way, both in the spherically sym…