Tan's contact is a quantity that unifies many different properties of a low-temperature gas with short-range interactions, from its momentum distribution to its spatial two-body correlation function. ...Here, we use a Ramsey interferometric method to realize experimentally the thermodynamic definition of the two-body contact, i.e., the change of the internal energy in a small modification of the scattering length. Our measurements are performed on a uniform two-dimensional Bose gas of
Rb atoms across the Berezinskii-Kosterlitz-Thouless superfluid transition. They connect well to the theoretical predictions in the limiting cases of a strongly degenerate fluid and of a normal gas. They also provide the variation of this key quantity in the critical region, where further theoretical efforts are needed to account for our findings.
A fluid is said to be scale invariant when its interaction and kinetic energies have the same scaling in a dilation operation. In association with the more general conformal invariance, scale ...invariance provides a dynamical symmetry which has profound consequences both on the equilibrium properties of the fluid and its time evolution. Here we investigate experimentally the far-from-equilibrium dynamics of a cold two-dimensional rubidium Bose gas. We operate in the regime where the gas is accurately described by a classical field obeying the Gross-Pitaevskii equation, and thus possesses a dynamical symmetry described by the Lorentz group SO(2,1). With the further simplification provided by superfluid hydrodynamics, we show how to relate the evolutions observed for different initial sizes, atom numbers, trap frequencies, and interaction parameters by a scaling transform. Finally, we show that some specific initial shapes—uniformly filled triangles or disks—may lead to a periodic evolution corresponding to a novel type of breather for the two-dimensional Gross-Pitaevskii equation.
Abstract
When two Bose–Einstein condensates—labelled 1 and 2—overlap spatially, the equilibrium state of the system depends on the miscibility criterion for the two fluids. Here, we theoretically ...focus on the non-miscible regime in two spatial dimensions and explore the properties of the localized wave packet formed by the minority component 2 when immersed in an infinite bath formed by component 1. We address the zero-temperature regime and describe the two-fluid system by coupled classical field equations. We show that such a wave packet exists only for an atom number
N
2
above a threshold value corresponding to the Townes soliton state. We identify the regimes where this localized state can be described by an effective single-field equation up to the droplet case, where component 2 behaves like an incompressible fluid. We study the near-equilibrium dynamics of the coupled fluids, which reveals specific parameter ranges for the existence of localized excitation modes.
Most experimental observations of solitons are limited to one-dimensional (1D) situations, where they are naturally stable. For instance, in 1D cold Bose gases, they exist for any attractive ...interaction strength g and particle number N. By contrast, in two dimensions, solitons appear only for discrete values of gN, the so-called Townes soliton being the most celebrated example. Here, we use a two-component Bose gas to prepare deterministically such a soliton: Starting from a uniform bath of atoms in a given internal state, we imprint the soliton wave function using an optical transfer to another state. We explore various interaction strengths, atom numbers, and sizes and confirm the existence of a solitonic behavior for a specific value of gN and arbitrary sizes, a hallmark of scale invariance.
The single-station microtremor horizontal-to-vertical spectral ratio (MHVSR) method was initially proposed to retrieve the site amplification function and its resonance frequencies produced by ...unconsolidated sediments overlying high-velocity bedrock. Presently, MHVSR measurements are predominantly conducted to obtain an estimate of the fundamental site frequency at sites where a strong subsurface impedance contrast exists. Of the earthquake site characterization methods presented in this special issue, the MHVSR method is the furthest behind in terms of consensus towards standardized guidelines and commercial use. The greatest challenges to an international standardization of MHVSR acquisition and analysis are (1) the
what
— the underlying composition of the microtremor wavefield is site-dependent, and thus, the appropriate theoretical (forward) model for inversion is still debated; and (2) the
how
— many factors and options are involved in the data acquisition, processing, and interpretation stages. This paper reviews briefly a historical development of the MHVSR technique and the physical basis of an MHVSR (the
what
). We then summarize recommendations for MHVSR acquisition and analysis (the
how
). Specific sections address MHVSR interpretation and uncertainty assessment.
In atomic systems, clock states feature a zero projection of the total angular momentum and thus a low sensitivity to magnetic fields. This makes them widely used for metrological applications like ...atomic fountains or gravimeters. Here, we show that a mixture of two such nonmagnetic states still displays magnetic dipole-dipole interactions comparable to the one expected for the other Zeeman states of the same atomic species. Using high-resolution spectroscopy of a planar gas of ^{87}Rb atoms with a controlled in plane shape, we explore the effective isotropic and extensive character of these interactions and demonstrate their tunability. Our measurements set strong constraints on the relative values of the s-wave scattering lengths a_{ij} involving the two clock states.
This is the first part of a three-paper review of homogenization and topology optimization, viewed from an engineering standpoint and with the ultimate aim of clarifying the ideas so that interested ...researchers can easily implement the concepts described. In the first paper we focus on the theory of the homogenization method where we are concerned with the main concepts and derivation of the equations for computation of effective constitutive parameters of complex materials with a periodic micro structure. Such materials are described by the base cell, which is the smallest repetitive unit of material, and the evaluation of the effective constitutive parameters may be carried out by analysing the base cell alone. For simple microstructures this may be achieved analytically, whereas for more complicated systems numerical methods such as the finite element method must be employed. In the second paper, we consider numerical and analytical solutions of the homogenization equations. Topology optimization of structures is a rapidly growing research area, and as opposed to shape optimization allows the introduction of holes in structures, with consequent savings in weight and improved structural characteristics. The homogenization approach, with an emphasis on the optimality criteria method, will be the topic of the third paper in this review.
A new isogeometrical procedure for optimization of material composition of functionally graded structures in thermo-mechanical processes is introduced. The proposed method employs a generalized form ...of the standard isogeometric analysis method, allowing for gradation of material properties through patches. The variations of material properties are captured in a fully isogeometric formulation using the same NURBS basis functions employed for construction of the geometry and approximation of the solution. Subsequently, the applicates of control points that define the surfaces of volume fractions of the constituents are considered as the design variables and obtained by solving the optimization problem using a mathematical programming algorithm. Some numerical examples under thermal and mechanical loadings are considered to demonstrate the performance and applicability of the proposed method. Comparison of the obtained results with those of the other existing approaches such as finite elements and meshfree methods verifies the presented results. It will be seen that the proposed procedure considerably removes the difficulties of the existing methods and provides a promising tool for material design of functionally graded structures.
Hydraulic properties of soils, particularly water retention, are key for appropriate management of semiarid soils. Very few pedotransfer functions (PTFs) have been developed to predict these ...properties for soils of Mediterranean regions, where data are particularly scarce. We investigated the transferability of PTFs to semiarid soils. The quality of the prediction was compared to that for soils originating from temperate regions for which most PTFs were developed. We used two soil data sets: one from the Paris basin (French data set, n = 30) and a Syrian data set (n = 30). Soil samples were collected in winter when the water content was near field capacity. Composition and water content of the samples were determined at seven water potentials. Continuous‐ and class‐PTFs developed using different predictors were tested using the two data sets and their performance compared to those developed using artificial neural networks (ANN). The best performance and transferability of the PTFs for both data sets used soil water content at field capacity as predictor after stratification by texture. The quality of prediction was similar to that for ANN‐PTFs. Continuous‐ and class‐PTFs may be transferable to other countries with performances that vary according to their ability to account for variation in soil composition and structure. Taking into account predictors of composition (particle size distribution, texture, organic carbon content) and structure (bulk density, porosity, field capacity) did not lead to a better performance or the best transferability potential.
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