31,962 research outputs found
Lattice Interferometer for Ultra-Cold Atoms
We demonstrate an atomic interferometer based on ultra-cold atoms released
from an optical lattice. This technique yields a large improvement in signal to
noise over a related interferometer previously demonstrated. The interferometer
involves diffraction of the atoms using a pulsed optical lattice. For short
pulses a simple analytical theory predicts the expected signal. We investigate
the interferometer for both short pulses and longer pulses where the analytical
theory break down. Longer pulses can improve the precision and signal size. For
specific pulse lengths we observe a coherent signal at times that differs
greatly from what is expected from the short pulse model. The interferometric
signal also reveals information about the dynamics of the atoms in the lattice.
We investigate the application of the interferometer for a measurement of
that together with other well known constants constitutes a measurement
of the fine structure constant
A hybrid perturbation Galerkin technique with applications to slender body theory
A two step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed
Resonant frequency calculations using a hybrid perturbation-Galerkin technique
A two-step hybrid perturbation Galerkin technique is applied to the problem of determining the resonant frequencies of one or several degree of freedom nonlinear systems involving a parameter. In one step, the Lindstedt-Poincare method is used to determine perturbation solutions which are formally valid about one or more special values of the parameter (e.g., for large or small values of the parameter). In step two, a subset of the perturbation coordinate functions determined in step one is used in Galerkin type approximation. The technique is illustrated for several one degree of freedom systems, including the Duffing and van der Pol oscillators, as well as for the compound pendulum. For all of the examples considered, it is shown that the frequencies obtained by the hybrid technique using only a few terms from the perturbation solutions are significantly more accurate than the perturbation results on which they are based, and they compare very well with frequencies obtained by purely numerical methods
Investigating a hybrid perturbation-Galerkin technique using computer algebra
A two-step hybrid perturbation-Galerkin method is presented for the solution of a variety of differential equations type problems which involve a scalar parameter. The resulting (approximate) solution has the form of a sum where each term consists of the product of two functions. The first function is a function of the independent field variable(s) x, and the second is a function of the parameter lambda. In step one the functions of x are determined by forming a perturbation expansion in lambda. In step two the functions of lambda are determined through the use of the classical Bubnov-Gelerkin method. The resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Bubnov-Galerkin methods applied separately, while combining some of the good features of each. In particular, the results can be useful well beyond the radius of convergence associated with the perturbation expansion. The hybrid method is applied with the aid of computer algebra to a simple two-point boundary value problem where the radius of convergence is finite and to a quantum eigenvalue problem where the radius of convergence is zero. For both problems the hybrid method apparently converges for an infinite range of the parameter lambda. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed
Hot-water aquifer storage: A field test
The basic water injection cycle used in a large-scale field study of heat storage in a confined aquifer near Mobile, Alabama is described. Water was pumped from an upper semi-confined aquifer, passed through a boiler where it was heated to a temperature of about 55 C, and injected into a medium sand confined aquifer. The injection well has a 6-inch (15-cm) partially-penetrating steel screen. The top of the storage formation is about 40 meters below the surface and the formation thickness is about 21 meters. In the first cycle, after a storage period of 51 days, the injection well was pumped until the temperature of the recovered water dropped to 33 c. At that point 55,300 cubic meters of water had been withdrawn and 66 percent of the injected energy had been recovered. The recovery period for the second cycle continued until the water temperature was 27.5 C and 100,100 cubic meters of water was recovered. At the end of the cycle about 90 percent of the energy injected during the cycle had been recovered
A hybrid perturbation-Galerkin method for differential equations containing a parameter
A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed
Passive scalar intermittency in low temperature helium flows
We report new measurements of turbulent mixing of temperature fluctuations in
a low temperature helium gas experiment, spanning a range of microscale
Reynolds number, , from 100 to 650. The exponents of the
temperature structure functions
are shown to saturate to for the highest
orders, . This saturation is a signature of statistics dominated by
front-like structures, the cliffs. Statistics of the cliff characteristics are
performed, particularly their width are shown to scale as the Kolmogorov length
scale.Comment: 4 pages, with 4 figure
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