Search results for "Equations"
showing 10 items of 955 documents
Uniqueness and reconstruction for the fractional Calder\'on problem with a single measurement
2020
We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many measurements. The method is again based on the strong uniqueness properties for the fractional equation, this time combined with a unique continuation principle from sets of measure zero. We also give a constructive procedure for determining an unknown potential from a single exterior measurement, based on constructive versions of the unique continuation result that involve different regularization schemes.
Dimensional analysis and upscaling of two-phase flow in porous media with piecewise constant heterogeneities
2004
Dimensional analysis of the traditional equations of motion for two-phase flow in porous media allows to quantify the influence of heterogeneities. The heterogeneities are represented by position dependent capillary entry pressures and position dependent permeabilities. Dimensionless groups quantifying the influence of random heterogeneities are identified. For the case of heterogeneities with piecewise constant constitutive parameters (e.g., permeabilities, capillary pressures) we find that the upscaling ratio defined as the ratio of system size and the scale at which the constitutive parameters are known has to be smaller than the fluctuation strength of the heterogeneities defined, e.g.,…
Exact treatment of operator difference equations with nonconstant and noncommutative coefficients
2013
We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.
Approximate Osher–Solomon schemes for hyperbolic systems
2016
This paper is concerned with a new kind of Riemann solvers for hyperbolic systems, which can be applied both in the conservative and nonconservative cases. In particular, the proposed schemes constitute a simple version of the classical Osher-Solomon Riemann solver, and extend in some sense the schemes proposed in Dumbser and Toro (2011) 19,20. The viscosity matrix of the numerical flux is constructed as a linear combination of functional evaluations of the Jacobian of the flux at several quadrature points. Some families of functions have been proposed to this end: Chebyshev polynomials and rational-type functions. Our schemes have been tested with different initial value Riemann problems f…
Kinetische untersuchungen zur strahleninduzierten festkörperpolymerisation von trioxan und tetroxan IV. Mitt. der Reihe “kinetische und morphologisch…
1971
Die strahlungsinduzierte Polymerisation von kristallinem Tetroxan und Trioxan wurde untersucht und der Einflus von Strahlendosis, Reaktionszeit und -temperatur auf den Umsatz und das Molekulargewicht der entstehenden POM, insbesondere bei der Nachpolymerisation, studiert. Die Zeit-Umsatz-Kurven fur die Nachpolymerisation laufen bei beiden Monomeren asymptotisch gegen einem Grenzwert des Umsatzes, der mit steigender Reaktionstemperatur ansteigt. Die Aktivierungsenergie der Nachpolymerisation wurde zu 24 ± 2 kcal/Mol fur Tetroxan und zu 36–38 kcal/Mol fur Trioxan bestimmt. Die Zeit(t)-Umsatz(x)-Kurven fur Tetroxan lassen sich durch die empirische Gleichung: beschreiben, wobei k1 und k2 Konsta…
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.
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.
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…
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.
Classical and quantum aspects of electric-magnetic duality rotations in curved spacetimes
2018
It is well known that the source-free Maxwell equations are invariant under electric-magnetic duality rotations, $\mathrm{F}\ensuremath{\rightarrow}\mathrm{F}\mathrm{cos}\ensuremath{\theta}+^{\ensuremath{\star}}\mathrm{F}\mathrm{sin}\ensuremath{\theta}$. These transformations are indeed a symmetry of the theory in the Noether sense. The associated constant of motion is the difference in the intensity between self-dual and anti-self-dual components of the electromagnetic field or, equivalently, the difference between the right and left circularly polarized components. This conservation law holds even if the electromagnetic field interacts with an arbitrary classical gravitational background.…