String dynamics near the photon sphere in Schwarzschild spacetime is considered on the basis of a perturbative approach with respect to a rescaled string tension as a small parameter. The perturbative string solution in the zeroth and first approximation is presented. The perturbative solution corresponds to a small deformation of the photon sphere in Schwarzschild spacetime. PACS number(s): 04...

We derive a Hamiltonian form of the fourth-order (extended) nonlinear Schrödinger equation (NLSE) in Klein–Gordon model with quadratic and cubic nonlinearities. This describes propagation envelope slowly modulated wave packets approximated by superposition fundamental, second, zeroth harmonics. Although extended NLSEs are not generally PDEs, derived here is PDE that preserves structure original...

New implementations of the Lévy–Leblond, zeroth-order regular approach ~ZORA! and spin-free Dirac equation are presented within the framework of the four-component relativistic program system DIRAC. This implementation allows systematic incorporation of relativistic effects at different levels of theory and corresponding computational cost. One of the possibilities of the new code is to neglect...

A mathematical model for peristaltic motion of nonlinear viscous flows with elastic free boundaries is introduced. An iterative numerical method is used to solve the free boundary problem. Long wave asymptotic expansion is developed and the zeroth order approximation is used as the numerical initial condition. The existence and uniqueness of the solution for the free boundary equation derived f...

We consider unconstrained stochastic optimization problems with no available gradient information. Such arise in settings from derivative-free simulation to reinforcement learning. propose an adaptive sampling quasi-Newton method where we estimate the gradients using finite differences of function evaluations within a common random number framework. develop modified versions norm test and inner...

We investigate the statistical parity of a class of chaos-generated noises on the escape of strongly damped particles out of a potential well. We show that statistical asymmetry in the chaotic fluctuations can lead to a skewed Maxwell-Boltzmann distribution in the well. Depending on the direction of skew, the Kramers escape rate is enhanced or suppressed accordingly. Based on the Perron-Frobeni...

This article focuses on the time-domain propagation of elastic waves through a 1D periodic medium that contains non-linear imperfect interfaces, i.e. interfaces exhibiting discontinuity in displacement and stress governed by constitutive relation. The array considered is generated a, possibly heterogeneous, cell repeated periodically bonded are associated with transmission conditions “spring–ma...

In the present paper the macroscopic limits of the kinetic model for interacting entities (individuals, organisms, cells) proposed in [3] are studied. The kinetic model is one–dimensional and entities are characterized by their position and orientation (+/-) with swarming interaction controlled by the sensitivity parameter γ. The macroscopic limits of the model are considered for solutions clos...

Despite considerable practical success in dealing with the gluon plasma, finite-temperature perturbation theory suffers at the fundamental level from infrared divergences discovered by Linde. However, if gauge or Gribov copies are properly eliminated from the physical state space, infrared modes are strongly suppressed. We describe the gluon plasma in zeroth order as a gas of free quasiparticle...

The fivebrane in M-theory comes equipped with a higher order gauge field which should have a formulation in terms of a 2-gerbe on the fivebrane. One can pose the question if the BV-quantization scheme for such a higher order gauge theory should differ from the usual BV-algebra structure. We give an algebraic argument that this should, indeed, be the case and a fourth order equation should appea...