Islands and Page curves for evaporating black holes in JT gravity

The effect of a CFT shockwave on the entanglement structure of an eternal black hole in Jackiw-Teitelboim gravity, that is in thermal equilibrium with a thermal bath, is considered. The shockwave carries energy and entropy into the black hole and heats the black hole up leading to evaporation and the eventual recovery of equilibrium. We find an analytical description of the entire relaxational process within the semiclassical high temperature regime. If the shockwave is inserted around the Page time then several scenarios are possible depending on the parameters. The Page time can be delayed or hastened and there can be more than one transition. The final entropy saddle has a quantum extremal surface that generically starts inside the horizon but at some later time moves outside. In general, increased shockwave energy and slow evaporation rate favour the extremal surface to be inside the horizon. The shockwave also disrupts the scrambling properties of the black hole. The same analysis is then applied to a shockwave inserted into the extremal black hole with similar conclusions.

Dielectric investigations of La-doped barium titanate

In the present paper results of the dielectric investigation of barium titanate (BaTiO3) doped with different concentrations of lanthanum are presented. Ceramic samples were prepared by the Pechini process. With increased doping the grain size of ceramics decreases from 2.5 ?m in pure samples down to 0.2 ?m in 0.5 mol% La - doped BaTiO3. Ceramics showed maximally enhanced dielectric permittivity around low-, room and high temperature phase transitions, which are the phase transitions of the pure BaTiO3. The Curie temperature, TC, is lowered by 30 K with increase of doping concentration to 0.5 mol% La. Dielectric spectra revealed three parts: low frequency part which is caused by conductivity process, middle frequency relaxational process part and high frequency relaxational/polar modes contribution.

A Relaxation Method for Simulating the Kinematics of Compound Nonlinear Mechanisms

This paper describes a relaxation-based method for simulating 2D and 3D compound kinematic mechanisms. The relaxational process iteratively propagates node motions and degrees of freedom throughout a given kinematic mechanism. While relaxation methods were classically used to solve static problems, we show that the propagation of displacements during the calculation process itself reveals the kinematics of the structure. The method is slower than approaches based on solving simultaneous differential equations of motion, but provides several advantages: It achieves a higher level of accuracy, is more robust in handling transient singularities and degeneracies of the mechanism, and can handle more complex compound mechanisms with many links in multiple entangled kinematic chains. It also allows straightforward introduction of linkages with nonlinear behaviors such as wrapping strings, hydraulics, actuators, contacts, and other arbitrary responses. The basic simulation algorithm is presented, and a number of applications are provided including robotics, design, and biomechanics.

Heterogeneous Microcomposite Materials Based on Porous Matrices and Liquid Crystals

Heterogeneous microcomposite materials based on porous matrices with randomly oriented, interconnected pores (porous glasses with average pore sizes of 100 Å and 1000 Å) and parallel cylindrical pores (Anopore membranes with pore diameters of 200 Å and 2000 Å) impregnated with liquid crystals (LC) were investigated by dynamic light scattering and dielectric spectroscopy. The physical properties of confined LC are very different from that of the bulk. One of the new properties among others observed for LC confined in porous matrices is the slow relaxational process which does not exist in the bulk LC and a wide spectrum of relaxation times (10−8 – 10)s which were established in both dynamic light scattering and dielectric experiments. We found that for LC dispersed in porous matrices with randomly distributed interconnected pores, the contribution to physical properties and observed behavior from interfacial layers dominates and almost completely determines low frequency relaxational process.

Slow Dynamics and Glass-Like Behavior of Liquid Crystals Dispersed in Nanoporous Media

ABSTRACTWe have investigated the dynamic behavior of liquid crystals (LC), which are not glass formers when in bulk form, confined in porous matrices with randomly oriented, interconnected pores as well as in parallel cylindrical pores with different pore sizes by photon correlation (time range: 20 ns-103s) and dielectric spectroscopies (frequencies: 0.1 Hz-1.5GHz). We observed that in random pores (pore size is 10 nm and 100 nm) LC does not crystallize at temperatures about 25° C below bulk crystallization temperature and the non-Debye relaxational processes studied by both photon correlation and dielectric experiments were found not to be frozen. Slow relaxational process which does not exist in bulk LC and a broad spectrum of relaxation times (10−8 − 10)s appear not only for LC in random pores but in cylindrical pores as well. However in matrices with random pores of 100 Å, glass-like behavior of slow mode (τ > 1ms) was observed. The relaxation time (determined in photon correlation experiment) of this slow process strongly increases when temperature decreases from 300 K up to 270 K varying from 0.2ms to 14 s and it's temperature dependence is described by the Vogel-Fulcher law.