Information transfer with a gravitating bath

Late-time dominance of entanglement islands plays a critical role in addressing the information paradox for black holes in AdS coupled to an asymptotic non-gravitational bath. A natural question is how this observation can be extended to gravitational systems. To gain insight into this question, we explore how this story is modified within the context of Karch-Randall braneworlds when we allow the asymptotic bath to couple to dynamical gravity. We find that because of the inability to separate degrees of freedom by spatial location when defining the radiation region, the entanglement entropy of radiation emitted into the bath is a time-independent constant, consistent with recent work on black hole information in asymptotically flat space. If we instead consider an entanglement entropy between two sectors of a specific division of the Hilbert space, we then find non-trivial time-dependence, with the Page time a monotonically decreasing function of the brane angle---provided both branes are below a particular angle. However, the properties of the entropy depend discontinuously on this angle, which is the first example of such discontinuous behavior for an AdS brane in AdS space.

Design of a New Hybrid Topology of WPT System to Achieve Load-Independent Constant-Current and Constant-Voltage Output

The usage of the Wireless Power Transfer (WPT) technique for charging lithium-ion (Li-ion) batteries of electric vehicles (EVs) is increasing rapidly. The Li-ion battery requires constant current (CC) followed by constant-voltage (CV) supply for efficient battery charging and to enhance its lifespan. However, it is hard to obtain CC and CV outputs due to the variation of battery resistance during charging. Moreover, a zero-phase angle (ZPA) of the input source is essential to improve the power transfer capability. Therefore, this paper proposes a new hybrid compensation topology to achieve load-independent CC and CV behavior of the WPT system along with ZPA. Two symmetrical coils have been used in the proposed WPT system as transmitter (Tx) and receiver (Rx) coils. A comprehensive mathematical analysis for achieving CC and CV characteristics as well as for power losses is carried out. A new hybrid compensation is designed by combining Series–Series (SS) and Inductor–Capacitor–Capacitor/Series (LCC-S) compensation topologies along with two additional switches. The proposed compensation works on single resonance frequency, and it is simple, reliable, and easy to implement with only one compensation capacitor from the Rx side. Simulations are performed, and a prototype is fabricated to verify the mathematical analysis and simulation results. The overall result shows that the mathematical analysis and simulations comply with the experimental results. Full load efficiencies of 90.33% and 88.91% are achieved in the CC and CV modes, respectively.

Thermal equation of state of post-aragonite CaCO3-Pmmn

Calcium carbonate (CaCO3) is one of the most abundant carbonates on Earth's surface and transports carbon to Earth's interior via subduction. Although some petrological observations support the preservation of CaCO3 in cold slabs to lower mantle depths, the geophysical properties and stability of CaCO3 at these depths are not known, due in part to complicated polymorphic phase transitions and lack of constraints on thermodynamic properties. Here we measured thermal equation of state of CaCO3-Pmmn, the stable polymorph of CaCO3 through much of the lower mantle, using synchrotron X-ray diffraction in a laser-heated diamond-anvil cell up to 75 GPa and 2200 K. The room-temperature compression data for CaCO3-Pmmn are fit with third-order Birch-Murnaghan equation of state, yielding KT0 = 146.7 (±1.9) GPa and K′0 = 3.4(±0.1) with V0 fixed to the value determined by ab initio calculation, 97.76 Å3. High-temperature compression data are consistent with zero-pressure thermal expansion αT = a0 + a1T with a0 = 4.3(±0.3)×10-5 K-1, a1 = 0.8(±0.2)×10-8 K-2, temperature derivative of the bulk modulus (∂KT/∂T)P = –0.021(±0.001) GPa/K; the Grüneisen parameter γ0 = 1.94(±0.02), and the volume independent constant q = 1.9(±0.3) at a fixed Debye temperature θ0 = 631 K predicted via ab initio calculation. Using these newly determined thermodynamic parameters, the density and bulk sound velocity of CaCO3-Pmmn and (Ca,Mg)-carbonate-bearing eclogite are quantitatively modeled from 30 to 80 GPa along a cold slab geotherm. With the assumption that carbonates are homogeneously mixed into the slab, the results indicate the presence of carbonates in the subducted slab is unlikely to be detected by seismic observations, and the buoyancy provided by carbonates has a negligible effect on slab dynamics.

On Pisier’s inequality for UMD targets

We prove an extension of Pisier’s inequality (1986) with a dimension-independent constant for vector-valued functions whose target spaces satisfy a relaxation of the UMD property.

Deep Brain Stimulation for Essential Tremor

Essential tremor (ET) is one of the most common movement disorders and can result in disabling symptoms that are refractory to standard medications. In 1997, the US Food and Drug Administration approved deep brain stimulation (DBS) of the ventral intermedius nucleus of the thalamus for treatment of ET. DBS often reduces or eliminates the need for medications to treat ET. Proper patient selection and expertise in DBS programming are critical to ensure optimal outcomes. Recent advances in DBS include directional current steering and multisource independent constant current to program each electrode with its own power source. This chapter discusses proper patient selection, programming guidelines, and clinical pearls in DBS for ET.