Szeg\"o kernel asymptotics and Morse inequalities on CR manifolds

We consider an abstract compact orientable Cauchy-Riemann manifold endowed with a Cauchy-Riemann complex line bundle. We assume that the manifold satisfies condition Y(q) everywhere. In this paper we obtain a scaling upper-bound for the Szeg\"o kernel on (0, q)-forms with values in the high tensor powers of the line bundle. This gives after integration weak Morse inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a refined spectral analysis we obtain also strong Morse inequalities which we apply to the embedding of some convex-concave manifolds.Comment: 40 pages, the constants in Theorems 1.1-1.8 have been modified by a multiplicative constant 1/2 ; v.2 is a final updat

Strain induced electrochemical behaviors of ionic liquid electrolytes in an electrochemical double layer capacitor: Insights from molecular dynamics simulations.

Electrochemical Double Layer Capacitors (EDLCs) with ionic liquid electrolytes outperform conventional ones using aqueous and organic electrolytes in energy density and safety. However, understanding the electrochemical behaviors of ionic liquid electrolytes under compressive/tensile strain is essential for the design of flexible EDLCs as well as normal EDLCs, which are subject to external forces during assembly. Despite many experimental studies, the compression/stretching effects on the performance of ionic liquid EDLCs remain inconclusive and controversial. In addition, there is hardly any evidence of prior theoretical work done in this area, which makes the literature on this topic scarce. Herein, for the first time, we developed an atomistic model to study the processes underlying the electrochemical behaviors of ionic liquids in an EDLC under strain. Constant potential non-equilibrium molecular dynamics simulations are conducted for EMIM BF4 placed between two graphene walls as electrodes. Compared to zero strain, low compression of the EDLC resulted in compromised performance as the electrode charge density dropped by 29%, and the performance reduction deteriorated significantly with a further increase in compression. In contrast, stretching is found to enhance the performance by increasing the charge storage in the electrodes by 7%. The performance changes with compression and stretching are due to changes in the double-layer structure. In addition, an increase in the value of the applied potential during the application of strain leads to capacity retention with compression revealed by the newly performed simulations. [Abstract copyright: © 2023 Author(s). Published under an exclusive license by AIP Publishing.

Irreversible vs reversible capacity fade of lithium-sulfur batteries during cycling: the effects of precipitation and shuttle

Lithium-sulfur batteries could deliver significantly higher gravimetric energy density and lower cost than Li-ion batteries. Their mass adoption, however, depends on many factors, not least on attaining a predictive understanding of the mechanisms that determine their performance under realistic operational conditions, such as partial charge/discharge cycles. This work addresses a lack of such understanding by studying experimentally and theoretically the response to partial cycling. A lithium-sulfur model is used to analyze the mechanisms dictating the experimentally observed response to partial cycling. The zero-dimensional electrochemical model tracks the time evolution of sulfur species, accounting for two electrochemical reactions, one precipitation/dissolution reaction with nucleation, and shuttle, allowing direct access to the true cell state of charge. The experimentally observed voltage drift is predicted by the model as a result of the interplay between shuttle and the dissolution bottleneck. Other features are shown to be caused by capacity fade. We propose a model of irreversible sulfur loss associated with shuttle, such as caused by reactions on the anode. We find a reversible and an irreversible contribution to the observed capacity fade, and verify experimentally that the reversible component, caused by the dissolution bottleneck, can be recovered through slow charging. This model can be the basis for cycling parameters optimization, or for identifying degradation mechanisms relevant in applications. The model code is released as Supplementary material B

Retarded long-range potentials for the alkali-metal atoms and a perfectly conducting wall

The retarded long-range potentials for hydrogen and alkali-metal atoms in their ground states and a perfectly conducting wall are calculated. The potentials are given over a wide range of atom-wall distances and the validity of the approximations used is established.Comment: RevTeX, epsf, 11 pages, 2 fig

Review—meta-review of fire safety of lithium-ion batteries: industry challenges and research contributions

The Lithium-ion battery (LIB) is an important technology for the present and future of energy storage, transport, and consumer electronics. However, many LIB types display a tendency to ignite or release gases. Although statistically rare, LIB fires pose hazards which are significantly different to other fire hazards in terms of initiation route, rate of spread, duration, toxicity, and suppression. For the first time, this paper collects and analyses the safety challenges faced by LIB industries across sectors, and compares them to the research contributions found in all the review papers in the field. The comparison identifies knowledge gaps and opportunities going forward. Industry and research efforts agree on the importance of understanding thermal runaway at the component and cell scales, and on the importance of developing prevention technologies. But much less research attention has been given to safety at the module and pack scales, or to other fire protection layers, such as compartmentation, detection or suppression. In order to close the gaps found and accelerate the arrival of new LIB safety solutions, we recommend closer collaborations between the battery and fire safety communities, which, supported by the major industries, could drive improvements, integration and harmonization of LIB safety across sectors

Prospects for p-wave paired BCS states of fermionic atoms

We present theoretical prospects for creating p-wave paired BCS states of magnetic trapped fermionic atoms. Based on our earlier proposal of using dc electric fields to control both the strength and anisotropic characteristic of atom-atom interaction and our recently completed multi-channel atomic collision calculations we discover that p-wave pairing with $^{40}$K and $^{82,84,86}$Rb in the low field seeking maximum spin polarized state represent excellent choices for achieving superfluid BCS states; and may be realizable with current technology in laser cooling, magnetic trapping, and evaporative/sympathetic cooling, provided the required strong electric field can be applied. We also comment on the prospects of similar p-wave paired BCS states in $^{6}$Li, and more generally on creating other types exotic BCS states. Our study will open a new area in the vigorous pursuit to create a quantum degenerate fermionic atom vapor.Comment: to be publishe

Classical Scattering for a driven inverted Gaussian potential in terms of the chaotic invariant set

We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate Poincare surface of section. We find the development parameters that describe the hyperbolic component of the chaotic invariant set. In addition, we show that the hierarchical structure of the fractal set of singularities of the scattering functions is the same as the structure of the chaotic invariant set. Finally, we construct a symbolic encoding of the hierarchical structure of the set of singularities of the scattering functions and use concepts from the thermodynamical formalism to obtain one of the measures of chaos of the fractal set of singularities, the topological entropy.Comment: accepted in Phy. Rev.

Cooper Pairing in Ultracold K-40 Using Feshbach Resonances

We point out that the fermionic isotope K-40 is a likely candidate for the formation of Cooper pairs in an ultracold atomic gas. Specifically, in an optical trap that simultaneously traps the spin states |9/2,-9/2> and |9/2,-7/2>, there exists a broad magnetic field Feshbach resonance at B = 196 gauss that can provide the required strong attractive interaction between atoms. An additional resonance, at B = 191 gauss, could generate p-wave pairing between identical |9/2,-7/2> atoms. A Cooper-paired degenerate Fermi gas could thus be constructed with existing ultracold atom technology.Comment: 4 pages, 2 figs, submitted to Phys. Rev.

Hydrodynamic excitations of trapped dipolar fermions

A single-component Fermi gas of polarized dipolar particles in a harmonic trap can undergo a mechanical collapse due to the attractive part of the dipole-dipole interaction. This phenomenon can be conveniently manipulated by the shape of the external trapping potential. We investigate the signatures of the instability by studying the spectrum of low-lying collective excitations of the system in the hydrodynamic regime. To this end, we employ a time-dependent variational method as well as exact numerical solutions of the hydrodynamic equations of the system.Comment: 4 pages, 2 eps figures, final versio

Spin instabilities and quantum phase transitions in integral and fractional quantum Hall states

The inter-Landau-level spin excitations of quantum Hall states at filling factors nu=2 and 4/3 are investigated by exact numerical diagonalization for the situation in which the cyclotron (hbar*omega_c) and Zeeman (E_Z) splittings are comparable. The relevant quasiparticles and their interactions are studied, including stable spin wave and skyrmion bound states. For nu=2, a spin instability at a finite value of epsilon=hbar*omega_c-E_Z leads to an abrupt paramagnetic to ferromagnetic transition, in agreement with the mean-field approximation. However, for nu=4/3 a new and unexpected quantum phase transition is found which involves a gradual change from paramagnetic to ferromagnetic occupancy of the partially filled Landau level as epsilon is decreased.Comment: 4 pages, 5 figures, submitted to Phys.Rev.Let