Related papers: Closed Form Expressions for the Potentials and Acc…
We have developed a two-dimensional orbit averaged Fokker-Planck model of stellar clusters which expands on spherically symmetric one-dimensional models to include rotation and ellipticity. Physical effects such as collisions, finite…
We show that an arbitrary probability distribution can be represented in exponential form. In physical contexts, this implies that the equilibrium distribution of any classical or quantum dynamical system is expressible in grand canonical…
Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers…
The atomic cluster expansion (Drautz, Phys. Rev. B 99, 014104 (2019)) is extended in two ways, the modelling of vectorial and tensorial atomic properties and the inclusion of atomic degrees of freedom in addition to the positions of the…
This contribution compiles the benefits of lattice symmetry in the context of closed orbit correction. A symmetric arrangement of BPMs and correctors results in structured orbit response matrices of Circulant or block Circulant type. These…
Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…
We consider density functionals for exchange and correlation energies in two-dimensional systems. The functionals are constructed by making use of exact constraints for the angular averages of the corresponding exchange and correlation…
It is shown that in general relativity some static metrics are able to simulate oscillatory motions. Their form depends on two arbitrary real parameters which determine the specific oscillation modes. The conclusion is that these metrics…
According to the classification scheme of the generalized random matrix ensembles, we present various kinds of concrete examples of the generalized ensemble, and derive their joint density functions in an unified way by one simple formula…
Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…
Toroidal structures are a common feature in a wide variety of astrophysical objects, including dusty tori in AGNs, rings in galaxies, protoplanetary disks, and others. The matter distribution in such structures is not homogeneous and can be…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
We derive a closed-form expression of the magnetic field of a finite-size current sheet and use it to calculate the field of permanent magnets, which are modeled through their surface current densities. We illustrate the method by…
We present an explicit formula for the expected value of a product of several independent symplectically invariant matrices in which the trace and real part function may be applied, possibly to different subexpressions. This takes the form…
The rosette-shaped motion of a particle in a central force field is known to be classically solvable by quadratures. We present a new approach of describing and characterizing such motion based on the eccentricity vector of the two body…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
A new formula for the gravitational potential of flattened systems is proposed. It is a modification of the Miyamoto-Nagai potential and should be applied to very flattened systems, exponential discs as a typical example. The resulting…
For any MONDian extended theory of gravity where the rotation curves of spiral galaxies are explained through a change in physics rather than the hypothesis of dark matter, a generic dynamical behavior is expected for pressure supported…
We present a novel way of modeling common envelope evolution in binary and few-body systems. We consider the common envelope inspiral as driven by a drag force with a power-law dependence in relative distance and velocity. The orbital…
This paper provides closed-form expansions for the log-likelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure…