scholarly journals Analytical study of the sth-order perturbative corrections to the solution to a one-dimensional harmonic oscillator perturbed by a spatially power-law potential Vper(x) = λxα

AIP Advances ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 085310
Author(s):  
Tran Duong Anh-Tai ◽  
Duc T. Hoang ◽  
Thu D. H. Truong ◽  
Chinh Dung Nguyen ◽  
Le Ngoc Uyen ◽  
...  
Keyword(s):  
Harmonic Oscillator ◽  
Power Law ◽  
Analytical Study ◽  
One Dimensional ◽  
Perturbative Corrections

Transient convective diffusion to a uniformly accessible surface under aparent slip conditions

1991 ◽  
Vol 56 (2) ◽  
pp. 334-343
Author(s):  
Ondřej Wein
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Convective Diffusion ◽  
Active Surface ◽  
Velocity Profiles ◽  
One Dimensional ◽  
Slip Conditions ◽  
Accessible Surface ◽  
Diffusion Problems

Analytical solutions are given to a class of unsteady one-dimensional convective-diffusion problems assuming power-law velocity profiles close to the transport-active surface.

scholarly journals Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps

2015 ◽  
Vol 114 (12) ◽  
Author(s):  
A. S. Campbell ◽  
D. M. Gangardt ◽  
K. V. Kheruntsyan
Keyword(s):  
Power Law ◽  
Bose Gas ◽  
Sudden Expansion ◽  
One Dimensional

scholarly journals Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

2013 ◽  
Vol 88 (13) ◽  
Author(s):  
Alejandro M. Lobos ◽  
Masaki Tezuka ◽  
Antonio M. García-García
Keyword(s):  
Power Law ◽  
Phase Coherence ◽  
Electron Hopping ◽  
One Dimensional

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

scholarly journals Critical flow and dissipation in a quasi–one-dimensional superfluid

2015 ◽  
Vol 1 (4) ◽  
pp. e1400222 ◽  
Author(s):  
Pierre-François Duc ◽  
Michel Savard ◽  
Matei Petrescu ◽  
Bernd Rosenow ◽  
Adrian Del Maestro ◽  
...  
Keyword(s):  
Power Law ◽  
Capillary Flow ◽  
Three Dimensional ◽  
Universality Class ◽  
Superfluid State ◽  
One Dimensional ◽  
Flow Experiment ◽  
20 Nm ◽  
Bulk Behavior ◽  
Superfluid Velocity

In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of 4He belongs to the same three-dimensional (3D) O(2) universality class as the onset of ferromagnetism in a lattice of classical spins with XY symmetry. Below the transition, the superfluid density ρs and superfluid velocity vs increase as a power law of temperature described by a universal critical exponent that is constrained to be identical by scale invariance. As the dimensionality is reduced toward 1D, it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single 30-nm-long nanopores with radii ranging down from 20 to 3 nm. As the pore size is reduced toward the 1D limit, we observe the following: (i) a suppression of the pressure dependence of the superfluid velocity; (ii) a temperature dependence of vs that surprisingly can be well-fitted by a power law with a single exponent over a broad range of temperatures; and (iii) decreasing critical velocities as a function of decreasing radius for channel sizes below R ≃ 20 nm, in stark contrast with what is observed in micrometer-sized channels. We interpret these deviations from bulk behavior as signaling the crossover to a quasi-1D state, whereby the size of a critical topological defect is cut off by the channel radius.

An Analytical Study of Cryosurgery in the Lung

1992 ◽  
Vol 114 (4) ◽  
pp. 467-472 ◽  
Author(s):  
J. C. Bischof ◽  
J. Bastacky ◽  
B. Rubinsky
Keyword(s):  
Finite Difference ◽  
Analytical Study ◽  
Outer Boundary ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Thermal Phenomenon ◽  
Healthy Lung Tissue ◽  
Close Form ◽  
Finite Difference Techniques ◽  
Healthy Lung

The process of freezing in healthy lung tissue and in tumors in the lung during cryosurgery was modeled using one-dimensional close form techniques and finite difference techniques to determine the temperature profiles and the propagation of the freezing interface in the tissue. A thermal phenomenon was observed during freezing of lung tumors embedded in healthy tissue, (a) the freezing interface suddenly accelerates at the transition between the tumor and the healthy lung, (b) the frozen tumor temperature drops to low values once the freezing interface moves into the healthy lung, and (c) the outer boundary temperature has a point of sharp inflection corresponding to the time at which the tumor is completely frozen.

scholarly journals Non-power-law universality in one-dimensional quasicrystals

2018 ◽  
Vol 98 (13) ◽  
Author(s):  
Attila Szabó ◽  
Ulrich Schneider
Keyword(s):  
Power Law ◽  
One Dimensional
Sign in / Sign up

Export Citation Format

Share Document