Search results for "Mathematical physics"
showing 10 items of 2687 documents
Statistische Ableitung der Grenzgesetze für verdünnte Lösungen bei Verschiedenheit der Molvolumina (Zur statistischen Theorie makromolekularer Lösung…
1947
Abstract Die Mischungsentropie einer binären Lösung, deren Komponenten verschiedene Mol-volumina haben, wird unter der Voraussetzung, daß die Moleküle kugelförmig sind, molekularstatistisch abgeleitet. Es zeigt sich, daß in diesem Fall die Verdünnungs-entropie höher ist als bei Gleichheit der Molvolumina. Bei kleinen Konzentrationen der höhermolekularen Komponente erhält man ein Korrekturglied, das ungefähr der van der W a a 1 s sehen Volumkorrektur entspricht. Bei verschwindender Konzen-tration geht die Gleichung für den osmotischen Druck in die v a n t'H o f f sehe über. Es wird untersucht, inwieweit man ein gitterartiges Modell für die molekularstati-stische Ableitung der Eigenschaften v…
An ecological dynamics rationale to explain home advantage in professional football
2016
Despite clear findings, research on home advantage in team sports lacks a comprehensive theoretical rationale for understanding why this phenomenon is so compelling. The aim of this study was to provide an explanatory theoretical rationale in ecological dynamics for the influence of home advantage observed in research on professional football. We recorded 30 competitive matches and analyzed 13958 passes, from one highly successful team in the Portuguese Premier League, during season 2010/2011. Performance data were analyzed using the Match Analysis Software—Amisco[Formula: see text] (version 3.3.7.25), allowing us to characterize team activity profiles. Results were interpreted from an ecol…
Non-hermitian operator modelling of basic cancer cell dynamics
2018
We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth.
Relative velocities, geometry, and expansion of space
2012
What does it mean to say that space expands? One approach to this question is the study of relative velocities. In this context, a non local test particle is "superluminal" if its relative velocity exceeds the local speed of light of the observer. The existence of superluminal relative velocities of receding test particles, in a particular cosmological model, suggests itself as a possible criterion for expansion of space in that model. In this point of view, superluminal velocities of distant receding galaxy clusters result from the expansion of space between the observer and the clusters. However, there is a fundamental ambiguity that must be resolved before this approach can be meaningful…
The combinatorics of the SU(2) black hole entropy in loop quantum gravity
2009
We use the combinatorial and number-theoretical methods developed in previous work by the authors to study black hole entropy in the new proposal put forward by Engle, Noui and Perez. Specifically we give the generating functions relevant for the computation of the entropy and use them to derive its asymptotic behavior including the value of the Immirzi parameter and the coefficient of the logarithmic correction.
Some Improvements on Relativistic Positioning Systems
2018
[EN] We make some considerations about Relativistic Positioning Systems (RPS). Four satellites are needed to position a user. First of all we define the main concepts. Errors should be taken into account. Errors depend on the Jacobian transformation matrix. Its Jacobian is proportional to the tetrahedron volume whose vertexes are the four tips of the receiver-satellite unit vectors. If the four satellites are seen by the user on a circumference in the sky, then, the Jacobian and the tetrahedron volume vanish. The users we consider are spacecraft. Spacecraft to be positioned cannot be close to a null Jacobian satellites-user configuration. These regions have to be avoided choosing an appropr…
Geometric inequivalence of metric and Palatini formulations of General Relativity
2020
Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, K≡R R , can be set to vanish everywhere. This puts forward that the divergence of curvature scalars may, in some cases, be avoided by a gauge transformation of the …
Non-Local Scattering Kernel and the Hydrodynamic Limit
2007
In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier-Stokes equations.
Non-equivariant cylindrical contact homology
2013
It was pointed out by Eliashberg in his ICM 2006 plenary talk that the integrable systems of rational Gromov-Witten theory very naturally appear in the rich algebraic formalism of symplectic field theory (SFT). Carefully generalizing the definition of gravitational descendants from Gromov-Witten theory to SFT, one can assign to every contact manifold a Hamiltonian system with symmetries on SFT homology and the question of its integrability arises. While we have shown how the well-known string, dilaton and divisor equations translate from Gromov-Witten theory to SFT, the next step is to show how genus-zero topological recursion translates to SFT. Compatible with the example of SFT of closed …
Recovery of time-dependent coefficients from boundary data for hyperbolic equations
2019
We study uniqueness of the recovery of a time-dependent magnetic vector-valued potential and an electric scalar-valued potential on a Riemannian manifold from the knowledge of the Dirichlet to Neumann map of a hyperbolic equation. The Cauchy data is observed on time-like parts of the space-time boundary and uniqueness is proved up to the natural gauge for the problem. The proof is based on Gaussian beams and inversion of the light ray transform on Lorentzian manifolds under the assumptions that the Lorentzian manifold is a product of a Riemannian manifold with a time interval and that the geodesic ray transform is invertible on the Riemannian manifold.