246 research outputs found
Reconstructing the thermal Green functions at real times from those at imaginary times
By exploiting the analyticity and boundary value properties of the thermal
Green functions that result from the KMS condition in both time and energy
complex variables, we treat the general (non-perturbative) problem of
recovering the thermal functions at real times from the corresponding functions
at imaginary times, introduced as primary objects in the Matsubara formalism.
The key property on which we rely is the fact that the Fourier transforms of
the retarded and advanced functions in the energy variable have to be the
`unique Carlsonian analytic interpolations' of the Fourier coefficients of the
imaginary-time correlator, the latter being taken at the discrete Matsubara
imaginary energies, respectively in the upper and lower half-planes. Starting
from the Fourier coefficients regarded as `data set', we then develop a method
based on the Pollaczek polynomials for constructing explicitly their analytic
interpolations.Comment: 23 pages, 2 figure
The Hausdorff moments in statistical mechanics
A new method for solving the Hausdorff moment problem is presented which makes use of Pollaczek polynomials. This problem is severely ill posed; a regularized solution is obtained without any use of prior knowledge. When the problem is treated in the L 2 space and the moments are finite in number and affected by noise or round‐off errors, the approximation converges asymptotically in the L 2 norm. The method is applied to various questions of statistical mechanics and in particular to the determination of the density of states. Concerning this latter problem the method is extended to include distribution valued densities. Computing the Laplace transform of the expansion a new series representation of the partition function Z(β) (β=1/k BT ) is obtained which coincides with a Watson resummation of the high‐temperature series for Z(β)
New Mechanics of Traumatic Brain Injury
The prediction and prevention of traumatic brain injury is a very important
aspect of preventive medical science. This paper proposes a new coupled
loading-rate hypothesis for the traumatic brain injury (TBI), which states that
the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an
impulsive loading that strikes the head in several coupled degrees-of-freedom
simultaneously. To show this, based on the previously defined covariant force
law, we formulate the coupled Newton-Euler dynamics of brain's micro-motions
within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt
dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brain's rapid
discontinuous deformations: translational dislocations and rotational
disclinations. Brain's dislocations and disclinations, caused by the
SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum
brain model.
Keywords: Traumatic brain injuries, coupled loading-rate hypothesis,
Euclidean jolt, coupled Newton-Euler dynamics, brain's dislocations and
disclinationsComment: 18 pages, 1 figure, Late
Excited States in 52Fe and the Origin of the Yrast Trap at I=12+
Excited states in 52Fe have been determined up to spin 10\hbar in the
reaction 28Si + 28Si at 115 MeV by using \gamma-ray spectroscopy methods at the
GASP array. The excitation energy of the yrast 10+ state has been determined to
be 7.381 MeV, almost 0.5 MeV above the well known \beta+-decaying yrast 12+
state, definitely confirming the nature of its isomeric character. The mean
lifetimes of the states have been measured by using the Doppler Shift
Attenuation method. The experimental data are compared with spherical shell
model calculations in the full pf-shell.Comment: 9 pages, RevTeX, 7 figures include
Structure of the icosahedral Ti-Zr-Ni quasicrystal
The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined
by invoking similarities to periodic crystalline phases, diffraction data and
the results from ab initio calculations. The structure is modeled by
decorations of the canonical cell tiling geometry. The initial decoration model
is based on the structure of the Frank-Kasper phase W-TiZrNi, the 1/1
approximant structure of the quasicrystal. The decoration model is optimized
using a new method of structural analysis combining a least-squares refinement
of diffraction data with results from ab initio calculations. The resulting
structural model of icosahedral Ti-Zr-Ni is interpreted as a simple decoration
rule and structural details are discussed.Comment: 12 pages, 8 figure
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