scholarly journals Mott-insulator-aided detection of ultra-narrow Feshbach resonances

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Manfred Mark ◽  
Florian Meinert ◽  
Katharina Lauber ◽  
Hanns-Christoph Nägerl
Keyword(s):  
Three Dimensional ◽  
Mott Insulator ◽  
Atomic Ensemble ◽  
Feshbach Resonances ◽  
High Background ◽  
Type Molecule ◽  
Theoretical Predictions ◽  
Magnetic Field Region ◽  
Atom Loss ◽  
Three Body

We report on the detection of extremely narrow Feshbach resonances by employing a Mott-insulating state for cesium atoms in a three-dimensional optical lattice. The Mott insulator protects the atomic ensemble from high background three-body losses in a magnetic field region where a broad Efimov resonance otherwise dominates the atom loss in bulk samples. Our technique reveals three ultra-narrow and previously unobserved Feshbach resonances in this region with widths below \approx 10\,\mu≈10μG, measured via Landau-Zener-type molecule formation and confirmed by theoretical predictions. For comparatively broader resonances we find a lattice-induced substructure in the respective atom-loss feature due to the interplay of tunneling and strong particle interactions. Our results provide a powerful tool to identify and characterize narrow scattering resonances, particularly in systems with complex Feshbach spectra. The observed ultra-narrow Feshbach resonances could be interesting candidates for precision measurements.

The Peak Overpressure Field Resulting From Shocks Emerging From Circular Shock Tubes

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
A. J. Newman ◽  
J. C. Mollendorf
Keyword(s):  
Shock Tube ◽  
Horizontal Plane ◽  
Three Dimensional ◽  
Polar Angle ◽  
Field Measurements ◽  
Initial Development ◽  
Theoretical Predictions ◽  
Mach Numbers ◽  
Tube Exit ◽  
Semi Empirical

A simple semi-empirical model for predicting the peak overpressure field that results when a shock emerges from a circular shock tube is presented and validated. By assuming that the shape of the expanding shock remains geometrically similar after an initial development period, an equation that describes the peak overpressure field in the horizontal plane containing the shock tube’s centerline was developed. The accuracy of this equation was evaluated experimentally by collecting peak overpressure field measurements along radials from the shock tube exit at 0 deg, 45 deg, and 90 deg over a range of shock Mach numbers from 1.15 to 1.45. It was found that the equation became more accurate at higher Mach numbers with percent differences between experimental measurements and theoretical predictions ranging from 1.1% to 3.6% over the range of Mach numbers considered. (1) Shocks do propagate in a geometrically similar manner after some initial development length over the range of Mach numbers considered here. (2) The model developed here gives reasonable predictions for the overpressure field from a shock emerging from a circular shock tube. (3) Shocks are expected to be completely symmetric with respect to the shock tube’s centerline, and hence, a three dimensional overpressure field may be predicted by the model developed here. (4) While there is a range of polar angle at which the shock shape may be described as being spherical with respect to the shock tube’s exit, this range does not encompass the entirety of the half space in front of the shock tube, and the model developed here is needed to accurately describe the entire peak overpressure field.

The Convergence of the H-P Version of the Finite Element Method with Quasi-Uniform Meshes for Three Dimensional Poisson Problems with Edge Singularity

2014 ◽  
Vol 644-650 ◽  
pp. 1551-1555
Author(s):  
Jian Ming Zhang ◽  
Yong He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weighted Sobolev Spaces ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Smooth Functions ◽  
Edge Singularity ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Element Method

This paper is concerned with the convergence of the h-p version of the finite element method for three dimensional Poisson problems with edge singularity on quasi-uniform meshes. First, we present the theoretical results for the convergence of the h-p version of the finite element method with quasi-uniform meshes for elliptic problems on polyhedral domains on smooth functions in the framework of Jacobi-weighted Sobolev spaces. Second, we investigate and analyze numerical results for three dimensional Poission problems with edge singularity. Finally, we verified the theoretical predictions by the numerical computation.

Effect of Finite Rotations on Gyroscopic Sensing Devices

1958 ◽  
Vol 25 (2) ◽  
pp. 210-213
Author(s):  
L. E. Goodman ◽  
A. R. Robinson
Keyword(s):  
Angular Velocity ◽  
Three Dimensional ◽  
Time History ◽  
Simple Method ◽  
Finite Rotations ◽  
Actual Solution ◽  
History Of ◽  
Body Components ◽  
Guidance Systems ◽  
Three Body

Abstract The well-known noncommutativity of three-dimensional finite rotations has long been a curiosity in mechanics since, in actual solution of dynamical problems, the angular velocity, which is conveniently representable as a vector, plays a more natural role. In modern inertial guidance systems, however, the orientation of a body in space, i.e., a rotation, is of primary engineering interest. In this paper a simple method of determining orientation from the time history of three body components of angular velocity is developed by means of a new theorem in kinematics. As a special case of this theorem it is shown that a gyro subjected to a regime of rotations which returns it to the original space orientation will, in general, produce a residual signal. It will have experienced a nonzero and easily calculated mean angular velocity about its input axis. Some implications of the theorem for the design of inertial guidance systems and for the testing of gyros are discussed.

Dynamics of Compliant Risers

1990 ◽  
Vol 34 (02) ◽  
pp. 123-135
Author(s):  
N. M. Patrikalakis ◽  
G. A. Kriezis ◽  
H. N. Gursoy ◽  
T. Maekawa
Keyword(s):  
Three Dimensional ◽  
Small Scale ◽  
Nonlinear Boundary Value Problems ◽  
Restoring Force ◽  
Numerical Solution Method ◽  
Quadratic Drag ◽  
Theoretical Predictions ◽  
Nonlinear Force ◽  
Nonlinear Static ◽  
Three Dimensional Configuration

The objective of this paper is first to formulate the three-dimensional dynamic equations of a compliant riser, idealized as a rotationally nonuniform rod, around a nonlinear static configuration with linearized restoring force and inertial components in the presence of general current and monochromatic wave excitation. Next, to harmonically linearize nonlinear forces such as quadratic drag for the general three-dimensional problem by minimizing the mean square error between the linear approximation and the nonlinear force. Finally, to present an efficient numerical solution method appropriate for nonlinear boundary-value problems with sharp boundary layers such as the problem at hand. Numerical examples and comparisons with time-domain solutions for a catenary riser with a three-dimensional configuration and a steep-wave riser are included. Comparisons of our theoretical predictions with experimental results obtained from a small-scale riser model are also summarized to evaluate our theoretical ability to predict the response of compliant riser systems.

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