976 research outputs found
Stability of flow of a thermoviscoelastic fluid between rotating coaxial circular cylinders
The stability problem of thermoviscoelastic fluid flow between rotating coaxial cylinders is investigated using nonlinear thermoviscoelastic constitutive equations due to Eringen and Koh. The velocity field is found to be identical with that of the classical viscous case and the case of the viscoelastic fluid, but the temperature and pressure fields are found to be different. By imposing some physically reasonable mechanical and geometrical restrictions on the flow, and by a suitable mathematical analysis, the problem is reduced to a characteristic value problem. The resulting problem is solved and stability criteria are obtained in terms of critical Taylor numbers. In general, it is found that thermoviscoelastic fluids are more stable than classical viscous fluids and viscoinelastic fluids under similar conditions
Can coarse-graining introduce long-range correlations in a symbolic sequence?
We present an exactly solvable mean-field-like theory of correlated ternary
sequences which are actually systems with two independent parameters. Depending
on the values of these parameters, the variance on the average number of any
given symbol shows a linear or a superlinear dependence on the length of the
sequence. We have shown that the available phase space of the system is made up
a diffusive region surrounded by a superdiffusive region. Motivated by the fact
that the diffusive portion of the phase space is larger than that for the
binary, we have studied the mapping between these two. We have identified the
region of the ternary phase space, particularly the diffusive part, that gets
mapped into the superdiffusive regime of the binary. This exact mapping implies
that long-range correlation found in a lower dimensional representative
sequence may not, in general, correspond to the correlation properties of the
original system.Comment: 10 pages including 1 figur
A growth walk model for estimating the canonical partition function of Interacting Self Avoiding Walk
We have explained in detail why the canonical partition function of
Interacting Self Avoiding Walk (ISAW), is exactly equivalent to the
configurational average of the weights associated with growth walks, such as
the Interacting Growth Walk (IGW), if the average is taken over the entire
genealogical tree of the walk. In this context, we have shown that it is not
always possible to factor the the density of states out of the canonical
partition function if the local growth rule is temperature-dependent. We have
presented Monte Carlo results for IGWs on a diamond lattice in order to
demonstrate that the actual set of IGW configurations available for study is
temperature-dependent even though the weighted averages lead to the expected
thermodynamic behavior of Interacting Self Avoiding Walk (ISAW).Comment: Revised version consisting of 12 pages (RevTeX manuscript, plus three
.eps figure files); A few sentences in the second paragraph on Page 4 are
rewritten so as to make the definition of the genealogical tree, , clearer. Also, the second equality of Eq.(1) on Page 4, and its
corresponding statement below have been remove
Siegert pseudostates: completeness and time evolution
Within the theory of Siegert pseudostates, it is possible to accurately
calculate bound states and resonances. The energy continuum is replaced by a
discrete set of states. Many questions of interest in scattering theory can be
addressed within the framework of this formalism, thereby avoiding the need to
treat the energy continuum. For practical calculations it is important to know
whether a certain subset of Siegert pseudostates comprises a basis. This is a
nontrivial issue, because of the unusual orthogonality and overcompleteness
properties of Siegert pseudostates. Using analytical and numerical arguments,
it is shown that the subset of bound states and outgoing Siegert pseudostates
forms a basis. Time evolution in the context of Siegert pseudostates is also
investigated. From the Mittag-Leffler expansion of the outgoing-wave Green's
function, the time-dependent expansion of a wave packet in terms of Siegert
pseudostates is derived. In this expression, all Siegert pseudostates--bound,
antibound, outgoing, and incoming--are employed. Each of these evolves in time
in a nonexponential fashion. Numerical tests underline the accuracy of the
method
Central extensions of current groups in two dimensions
In this paper we generalize some of these results for loop algebras and
groups as well as for the Virasoro algebra to the two-dimensional case. We
define and study a class of infinite dimensional complex Lie groups which are
central extensions of the group of smooth maps from a two dimensional
orientable surface without boundary to a simple complex Lie group G. These
extensions naturally correspond to complex curves. The kernel of such an
extension is the Jacobian of the curve. The study of the coadjoint action shows
that its orbits are labelled by moduli of holomorphic principal G-bundles over
the curve and can be described in the language of partial differential
equations. In genus one it is also possible to describe the orbits as conjugacy
classes of the twisted loop group, which leads to consideration of difference
equations for holomorphic functions. This gives rise to a hope that the
described groups should possess a counterpart of the rich representation theory
that has been developed for loop groups. We also define a two-dimensional
analogue of the Virasoro algebra associated with a complex curve. In genus one,
a study of a complex analogue of Hill's operator yields a description of
invariants of the coadjoint action of this Lie algebra. The answer turns out to
be the same as in dimension one: the invariants coincide with those for the
extended algebra of currents in sl(2).Comment: 17 page
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