1,910 research outputs found
Stability of a fermionic particle system with point interactions
We prove that a system of fermions interacting with an additional
particle via point interactions is stable if the ratio of the mass of the
additional particle to the one of the fermions is larger than some critical
. The value of is independent of and turns out to be less than
. This fact has important implications for the stability of the unitary
Fermi gas. We also characterize the domain of the Hamiltonian of this model,
and establish the validity of the Tan relations for all wave functions in the
domain.Comment: LaTeX, 29 pages, 2 figures; typos corrected, explanations and
references added; to appear in Commun. Math. Phy
Stability of the 2+2 fermionic system with point interactions
We give a lower bound on the ground state energy of a system of two fermions
of one species interacting with two fermions of another species via point
interactions. We show that there is a critical mass ratio m_c \approx 0.58 such
that the system is stable, i.e., the energy is bounded from below, for m \in
[m_c, m_c^{-1}]. So far it was not known whether this 2+2 system exhibits a
stable region at all or whether the formation of four-body bound states causes
an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our
result gives further evidence for the stability of the more general N+M system.Comment: LaTeX, 12 pages; typos corrected, references and 2 figures added; to
appear in Math. Phys. Anal. Geo
Triviality of a model of particles with point interactions in the thermodynamic limit
We consider a model of fermions interacting via point interactions, defined
via a certain weighted Dirichlet form. While for two particles the interaction
corresponds to infinite scattering length, the presence of further particles
effectively decreases the interaction strength. We show that the model becomes
trivial in the thermodynamic limit, in the sense that the free energy density
at any given particle density and temperature agrees with the corresponding
expression for non-interacting particles.Comment: LaTeX, 20 pages; final version, to appear in Lett. Math. Phy
Direct numerical simulation of turbulent channel flow up to
A direct numerical simulation of incompressible channel flow at =
5186 has been performed, and the flow exhibits a number of the characteristics
of high Reynolds number wall-bounded turbulent flows. For example, a region
where the mean velocity has a logarithmic variation is observed, with von
Karman constant . There is also a logarithmic
dependence of the variance of the spanwise velocity component, though not the
streamwise component. A distinct separation of scales exists between the large
outer-layer structures and small inner-layer structures. At intermediate
distances from the wall, the one-dimensional spectrum of the streamwise
velocity fluctuation in both the streamwise and spanwise directions exhibits
dependence over a short range in . Further, consistent with
previous experimental observations, when these spectra are multiplied by
(premultiplied spectra), they have a bi-modal structure with local peaks
located at wavenumbers on either side of the range.Comment: Under consideration for publication in J. Fluid Mec
A multigrid perspective on the parallel full approximation scheme in space and time
For the numerical solution of time-dependent partial differential equations,
time-parallel methods have recently shown to provide a promising way to extend
prevailing strong-scaling limits of numerical codes. One of the most complex
methods in this field is the "Parallel Full Approximation Scheme in Space and
Time" (PFASST). PFASST already shows promising results for many use cases and
many more is work in progress. However, a solid and reliable mathematical
foundation is still missing. We show that under certain assumptions the PFASST
algorithm can be conveniently and rigorously described as a multigrid-in-time
method. Following this equivalence, first steps towards a comprehensive
analysis of PFASST using block-wise local Fourier analysis are taken. The
theoretical results are applied to examples of diffusive and advective type
Characteristic eddy decomposition of turbulence in a channel
The proper orthogonal decomposition technique (Lumley's decomposition) is applied to the turbulent flow in a channel to extract coherent structures by decomposing the velocity field into characteristic eddies with random coefficients. In the homogeneous spatial directions, a generaliztion of the shot-noise expansion is used to determine the characteristic eddies. In this expansion, the Fourier coefficients of the characteristic eddy cannot be obtained from the second-order statistics. Three different techniques are used to determine the phases of these coefficients. They are based on: (1) the bispectrum, (2) a spatial compactness requirement, and (3) a functional continuity argument. Results from these three techniques are found to be similar in most respects. The implications of these techniques and the shot-noise expansion are discussed. The dominant eddy is found to contribute as much as 76 percent to the turbulent kinetic energy. In both 2D and 3D, the characteristic eddies consist of an ejection region straddled by streamwise vortices that leave the wall in the very short streamwise distance of about 100 wall units
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