First law of black hole in the gravitational electromagnetic system

After considering the quantum corrections of Einstein-Maxwell theory, the effective theory will contain some higher-curvature terms and nonminimally coupled electromagnetic fields. In this paper, we study the first law of black holes in the gravitational electromagnetic system with the Lagrangian ℒ(gab, Rabcd, Fab). Firstly, we calculate the Noether charge and the variational identity in this theory, and then generically derive the first law of thermodynamics for an asymptotically flat stationary-axisymmetric symmetric black hole without the requirement that the electromagnetic field is smooth on the bifurcation surface. Our results indicate that the first law of black hole thermodynamics might be valid for the Einstein-Maxwell theory with some quantum corrections in the effective region.

Anomalies in gravitational charge algebras of null boundaries and black hole entropy

We revisit the covariant phase space formalism applied to gravitational theories with null boundaries, utilizing the most general boundary conditions consistent with a fixed null normal. To fix the ambiguity inherent in the Wald-Zoupas definition of quasilocal charges, we propose a new principle, based on holographic reasoning, that the flux be of Dirichlet form. This also produces an expression for the analog of the Brown-York stress tensor on the null surface. Defining the algebra of charges using the Barnich-Troessaert bracket for open subsystems, we give a general formula for the central — or more generally, abelian — extensions that appear in terms of the anomalous transformation of the boundary term in the gravitational action. This anomaly arises from having fixed a frame for the null normal, and we draw parallels between it and the holographic Weyl anomaly that occurs in AdS/CFT. As an application of this formalism, we analyze the near-horizon Virasoro symmetry considered by Haco, Hawking, Perry, and Strominger, and perform a systematic derivation of the fluxes and central charges. Applying the Cardy formula to the result yields an entropy that is twice the Bekenstein-Hawking entropy of the horizon. Motivated by the extended Hilbert space construction, we interpret this in terms of a pair of entangled CFTs associated with edge modes on either side of the bifurcation surface.

INFLUENCE OF BUCKLING FORMS INTERACTION ON STIFFENED PLATE BEARING CAPACITY

The work is devoted to studying the influence of initial geometric imperfections on a value of the peak load for the compressed stiffened plate with the two-fold buckling load. The finite-element set MSC PATRAN – NASTRAN was used for solving the set tasks. When modelling the stiffened plate, flat four-unit elements were used. Geometric non-linearity was assumed for calculations. The plate material was regarded as perfectly elastic. Buckling forces of stiffened plate at the two-fold buckling load were calculated (simultaneous buckling failure on the form of the plate total bending and on the local form of wave formation in stiffened ribs). Equilibrium state curves, peak load decline curves depending on initial imperfection values and the bifurcation surface were plotted.

Bifurcation Control and Complex Dynamics in Field-Oriented Control of a PMSM

The general purpose of this paper is to develop new aspects of bifurcation structures in a 3D parametric space. Identification of generic bifurcation structures in former studies was based on the arrangement of bifurcation curves in the parameter plane. So by analogy to such studies, we define the bifurcation surface in 3D parameter space as the main feature of the said generic structures. The implementation of this idea is made on the permanent magnet synchronous machine (PMSM) whose speed is regulated with a field-oriented control (FOC). Sufficient conditions are given for the existence of three main bifurcations: limit point (LP), Hopf (H) and Bogdanov–Takens (BT). Starting from bifurcation curves traced in a parameter plane and changing a third parameter, a qualitative bifurcation surface is constructed in a 3D parametric space. This led to underline the increasing complexity of the bifurcation structures when dealing with more than two parameters. This study put into evidence not only the complex behavior of PMSM, but stands as a starting point for a new formalism on the bifurcation structures in a 3D parametric space.

Self-Excited Torsional Oscillations under Locked-Wheel Braking: Analysis and Experiments

ABSTRACT This paper analyzes the effect of tire/vehicle parameters, specifically of tire/suspension torsional stiffnesses, on the stability of self-excited tire torsional oscillations during locked-wheel braking events. Using a torsionally flexible tire-wheel model and a dynamic tire-ground friction model, two system models for tire oscillations are considered: with suspension torsional compliance included in one but excluded in the other. Bifurcation analysis is conducted on both systems to derive the effect of tire/vehicle parameters on the stability. For the system without suspension torsional compliance, it is highlighted that the primary cause of unstable self-excited oscillations is the “Stribeck” effect in tire-ground friction. Based on the parameters obtained experimentally, the bifurcation surface of vehicle velocity with respect to tire/suspension torsional stiffness is also given. The effect of tire/suspension torsional stiffness to the stability of tire torsional oscillation is qualitatively validated via comparisons between locked-wheel braking simulations and experiments with tires with different torsional stiffnesses.

Modeling study for oscillatory reaction of chlorite – iodide – ethyl acetoacetate

Chlorine dioxide based chemical oscillating behavior was modeled by a simple scheme consisting of three component reactions. Furthermore, little is known about the influence of the pH value. In this study, four component reactions were used to model the chlorite – iodide – ethyl acetoacetate oscillating reaction by dynamic analysis software. The oscillatory phenomenon is observed for concentration changes of triiodide ion, chlorite ion, and hydrogen ion. The initial concentration of ethyl acetoacetate, chlorite ion, iodide ion, and hydrogen ion has great influence on oscillations. The amplitude and number of oscillations are associated with the initial reactant concentrations. The equation of the reaction rate of triiodide ion, chlorite ion, or hydrogen ion changing with reaction time and initial concentrations in the oscillation stage was obtained. The bifurcation surface between oscillatory and nonoscillatory behavior with different pH values was obtained. The spatial zone for the occurrence of oscillation is reduced with an increase in the pH value. The range of oscillation as concentrations of chlorine dioxide, iodine, and ethyl acetoacetate is well described by an equation. There is a lower limit on ethyl acetoacetate initial concentration for oscillation. However, there is a higher limit on chlorine dioxide and iodine concentration for oscillation. The concentrations of chlorine dioxide and iodine for oscillation decrease with an increase in the pH value. The results provide new theoretical evidence of the importance of pH value, which can affect the bifurcation surface between oscillatory and nonoscillatory behavior.

HIGH ENERGY PARTICLE COLLISIONS NEAR THE BIFURCATION SURFACE

We consider generic nonextremal stationary dirty black holes. It is shown that in the vicinity of any bifurcation surface the energy of collision of two particles in the center of mass frame can grow unbound. This is a generic property that, in particular, includes collisions near the inner black hole horizon analyzed earlier by different methods. The similar results are also valid for cosmological horizons. The case of the de Sitter metric is discussed.

BIFURCATIONS OF HOMOCLINIC ORBIT CONNECTING TWO NONLEADING EIGENDIRECTIONS

Bifurcations of homoclinic orbit connecting the strong stable and strong unstable directions are investigated for four-dimensional system. The existence, numbers, co-existence and incoexistence of 1-homoclinic orbit, 2n-homoclinic orbit, 1-periodic orbit and 2n-periodic orbit are obtained, and the bifurcation surfaces (including codimension-1 homoclinic bifurcation surfaces, double periodic orbit bifurcation surfaces, homoclinic-doubling bifurcation surfaces, period-doubling bifurcation surfaces and codimension-2 triple periodic orbit bifurcation surface, and homoclinic and double periodic orbit bifurcation surface) and the existence regions are also located.