Quantum fluctuations in the BCS-BEC crossover of two-dimensional Fermi gases

We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the 2D mean-field theory indicates that the quantum fluctuations are much more pronounced than those in 3D. In this work, we show that the inclusion of the Gaussian quantum fluctuations naturally recovers the above features in both the BEC and the BCS limits. In the BEC limit, the missing logarithmic dependence on the boson chemical potential is recovered by the quantum fluctuations. Near the quantum phase transition from the vacuum to the BEC phase, we compare our equation of state with the known grand canonical equation of state of 2D Bose gases and determine the ratio of the composite boson scattering length $a_{\rm B}$ to the fermion scattering length $a_{\rm 2D}$. We find $a_{\rm B}\simeq 0.56 a_{\rm 2D}$, in good agreement with the exact four-body calculation. We compare our equation of state in the BCS-BEC crossover with recent results from the quantum Monte Carlo simulations and the experimental measurements and find good agreements.Comment: Published versio

A Mini Immersed Finite Element Method for Two-Phase Stokes Problems on Cartesian Meshes

This paper presents a mini immersed finite element (IFE) method for solving two- and three-dimensional two-phase Stokes problems on Cartesian meshes. The IFE space is constructed from the conventional mini element with shape functions modified on interface elements according to interface jump conditions, while keeping the degrees of freedom unchanged. Both discontinuous viscosity coefficients and surface forces are considered in the construction. The interface is approximated via discrete level set functions and explicit formulas of IFE basis functions and correction functions are derived, which make the IFE method easy to implement. The optimal approximation capabilities of the IFE space and the inf-sup stability and the optimal a priori error estimate of the IFE method are derived rigorously with constants independent of the mesh size and how the interface cuts the mesh. It is also proved that the condition number has the usual bound independent of the interface. Numerical experiments are provided to confirm the theoretical results

S-4-Chloro­phenyl 9,10-dihydro­acridine-9-carbothio­ate

In tricyclic fragment of the title mol­ecule, C20H14ClNOS, the central 1,4-dihydro­pyridine ring adopts a boat conformation while the two benzene rings form a dihedral angle of 17.38 (5)°. In the crystal structure, weak inter­molecular N—H⋯O hydrogen bonds link the mol­ecules into chains propagating along the b axis

A Comparison of Formal Methods for Evaluating the Language of Preference in Engineering Design

In design, as with many fields, the bases of decisions are generally not formally modeled but only talked or written about. The research problem addressed in this paper revolves around the problem of modeling the direct evaluation of design alternatives and their attributes as they are realized in linguistic communication. The question is what types of linguistic data provide the most reliable linguistic displays of preference and utility. The paper compares two formal methods for assessing a design team’s preferences for alternatives based on the team’s discussion: APPRAISAL and Preferential Probabilities from Transcripts (PPT). Results suggest that the two methods are comparable in their assessment of preferences. This paper also examines the nature of consistency in the way design teams consider the attributes of a design. Findings suggest that assessment of an attribute can change substantially over time.National Science Foundation (U.S.) (Award CMMI- 0900255)Australian Research Council (Discovery Projects funding scheme (project number DP1095601)

Self-supervised remote sensing feature learning: Learning Paradigms, Challenges, and Future Works

Deep learning has achieved great success in learning features from massive remote sensing images (RSIs). To better understand the connection between feature learning paradigms (e.g., unsupervised feature learning (USFL), supervised feature learning (SFL), and self-supervised feature learning (SSFL)), this paper analyzes and compares them from the perspective of feature learning signals, and gives a unified feature learning framework. Under this unified framework, we analyze the advantages of SSFL over the other two learning paradigms in RSIs understanding tasks and give a comprehensive review of the existing SSFL work in RS, including the pre-training dataset, self-supervised feature learning signals, and the evaluation methods. We further analyze the effect of SSFL signals and pre-training data on the learned features to provide insights for improving the RSI feature learning. Finally, we briefly discuss some open problems and possible research directions.Comment: 24 pages, 11 figures, 3 table

Optimal coherent control of CARS: signal enhancement and background elimination

The ability to enhance resonant signals and eliminate the non-resonant background is analyzed for Coherent Anti-Stokes Raman Scattering (CARS). The analysis is done at a specific frequency as well as for broadband excitation using femtosecond pulse-shaping techniques. An appropriate objective functional is employed to balance resonant signal enhancement against non-resonant background suppression. Optimal enhancement of the signal and minimization of the background can be achieved by shaping the probe pulse alone while keeping the pump and Stokes pulses in transform-limited-form (TLF). In some cases analytical forms for the probe pulse can be found, and numerical simulations are carried out for other circumstances. It is found that a good approximate solution for the optimal pulse in the two-pulse CARS is a superposition of linear and arctangent type phases for the pump. The well-known probe delay method is shown to be a quasi-optimal scheme for background suppression. The results should provide a basis to improve the performance of CARS spectroscopy and microscopy.Comment: 11 pages,10 figures, JC

Association of Affected Neurocircuitry With Deficit of Response Inhibition and Delayed Gratification in Attention Deficit Hyperactivity Disorder: A Narrative Review

The neural networks that constitute corticostriatothalamocortical circuits between prefrontal cortex and subcortical structure provide a heuristic framework for bridging gaps between neurocircuitry and executive dysfunction in attention deficit hyperactivity disorder (ADHD). “Cool” and “Hot” executive functional theory and the models of dual pathway are supposed to be applied within the neuropsychology of ADHD. The theoretical model elaborated response inhibition and delayed gratification in ADHD. We aimed to review and summarize the literature about the circuits on ADHD and ADHD-related comorbidities, as well as the effects of neurocircuitry on the executive dysfunction in ADHD