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In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved…
In dynamical systems limit cycles arise as a result of a Hopf bifurcation, after a control parameter has crossed its critical value. In this study we present a constructive method to produce dissipative dynamics which lead to stable…
We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical…
The structure of the interstellar medium in the central kpc region of a galaxy with a weak bar-like potential is investigated taking into account realistic cooling and heating processes and the self-gravity of the gas. Using high resolution…
We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. We treat the elliptic problem as a perturbation of the circular problem, where the perturbation parameter is the eccentricity of the…
Condensates of active particles such as cells form almost-crystalline lattices which play a central role in many biological systems. Typically, their properties have been determined merely by analogy to the rather trivial one-dimensional…
We investigate analytically a large-scale coherence in the orientation of galaxies embedded in two-dimensional sheet-like structures in the frame of the tidal torque theory. Assuming that the galaxy spin and the surrounding matter fields…
We are developing a 3D radiation hydrodynamics code to simulate the interaction of convection and pulsation in classical variable stars. One key goal is the ability to carry these simulations to full amplitude in order to compare them with…
We derive the complete set of geodesic equations for massive and massless, charged test particles of a five-dimensional, rotating and charged solution of the Einstein-Maxwell-Chern-Simons field equations in five-dimensional minimal gauged…
This study deals with the process and benefits of generating aerodynamic indicial-admittance functions with the support of computational fluid dynamics based on the Euler equations. A simple parametric analytical approximation is alongside…
We propose and experimentally validate the use of rotational echo responses for obtaining the degree of molecular alignment induced in a gas. The method is independent of various parameters that are hardly accessible in most experimental…
In this thesis are presented analytical results and numerical simulations concerning resonant processes in a frozen gas. This work was begun with the intent of modeling experiments involving energy transfer due to dipole-dipole interactions…
In this paper, we first develop a mathematical model for long-range, hydrophobic attraction between amphiphilic particles. The non-pairwise interactions follow from the first variation of a hydrophobic attraction domain functional. The…
The capture and inspiral of compact stellar masses into massive black holes is an important source of low-frequency gravitational waves (with frequencies of ~1-100mHz), such as those that might be detected by the planned Laser…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
The EFAR project is designed to measure the properties and peculiar motions of early-type galaxies in two distant regions. Here we describe the maximum likelihood algorithm we developed to investigate the correlations between the parameters…
We construct a simple symplectic map to study the dynamics of eccentric orbits in non-spherical potentials. The map offers a dramatic improvement in speed over traditional integration methods, while accurately representing the qualitative…
Recently, several femtosecond laser techniques have been developed that are capable of bringing gas molecules to extremely fast rotation in a very short time, while keeping their translational motion intact and relatively slow. We…
We describe a method for the numerical solution of the relativistic Euler equations which we have found to be both robust and efficient, and which has enabled us to simulate relativistic jets. The technique employs a solver of the…