384 research outputs found
Evolution of spherical cavitation bubbles: parametric and closed-form solutions
We present an analysis of the Rayleigh-Plesset equation for a three
dimensional vacuous bubble in water. In the simplest case when the effects of
surface tension are neglected, the known parametric solutions for the radius
and time evolution of the bubble in terms of a hypergeometric function are
briefly reviewed. By including the surface tension, we show the connection
between the Rayleigh-Plesset equation and Abel's equation, and obtain the
parametric rational Weierstrass periodic solutions following the Abel route. In
the same Abel approach, we also provide a discussion of the nonintegrable case
of nonzero viscosity for which we perform a numerical integrationComment: 9 pages, 5 figures, 14 references, version accepted for publication
at Phys. Fluid
Fundamentals of Flakeboard Manufacture: Viscoelastic Behavior of the Wood Component
Theories of the viscoelastic behavior of amorphous polymers are reviewed and are used to describe the density gradient formation in flakeboard. This technique utilizes measured temperature and gas pressure at discrete locations inside a flake mat during hot pressing to predict the glass transition temperature of wood as a function of press time. The difference between the flake temperature and the predicted glass transition temperature is a relative indicator of the amount of flake deformation and stress relaxation at a location in the mat. A knowledge of the stress history imposed in the mat is then used to relate flake deformation and stress relaxation to the formation of a density gradient. This analysis allows for a significant portion of the density gradient to develop after the hot press has closed. Experimental data for various density gradients support the theories presented here
The two-level atom laser: analytical results and the laser transition
The problem of the two-level atom laser is studied analytically. The
steady-state solution is expressed as a continued fraction, and allows for
accurate approximation by rational functions. Moreover, we show that the abrupt
change observed in the pump dependence of the steady-state population is
directly connected with the transition to the lasing regime. The condition for
a sharp transition to Poissonian statistics is expressed as a scaling limit of
vanishing cavity loss and light-matter coupling, , ,
such that stays finite and , where
is the rate of atomic losses. The same scaling procedure is also shown to
describe a similar change to Poisson distribution in the Scully-Lamb laser
model too, suggesting that the low-, low- asymptotics is of a more
general significance for the laser transition.Comment: 23 pages, 3 figures. Extended discussion of the paper aim (in the
Introduction) and of the results (Conclusions and Discussion). Results
unchange
Classical Noncommutative Electrodynamics with External Source
In a -noncommutative (NC) gauge field theory we extend the
Seiberg-Witten (SW) map to include the (gauge-invariance-violating) external
current and formulate - to the first order in the NC parameter -
gauge-covariant classical field equations. We find solutions to these equations
in the vacuum and in an external magnetic field, when the 4-current is a static
electric charge of a finite size , restricted from below by the elementary
length. We impose extra boundary conditions, which we use to rule out all
singularities, included, from the solutions. The static charge proves to
be a magnetic dipole, with its magnetic moment being inversely proportional to
its size . The external magnetic field modifies the long-range Coulomb field
and some electromagnetic form-factors. We also analyze the ambiguity in the SW
map and show that at least to the order studied here it is equivalent to the
ambiguity of adding a homogeneous solution to the current-conservation
equation
Excitons in narrow-gap carbon nanotubes
We calculate the exciton binding energy in single-walled carbon nanotubes
with narrow band gaps, accounting for the quasi-relativistic dispersion of
electrons and holes. Exact analytical solutions of the quantum relativistic
two-body problem are obtain for several limiting cases. We show that the
binding energy scales with the band gap, and conclude on the basis of the data
available for semiconductor nanotubes that there is no transition to an
excitonic insulator in quasi-metallic nanotubes and that their THz applications
are feasible.Comment: 11 pages, 3 figures. Several references and an additional appendix
adde
Solutions for certain classes of Riccati differential equation
We derive some analytic closed-form solutions for a class of Riccati equation
y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are
C^{\infty}-functions. We show that if \delta_n=\lambda_n
s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}=
\lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and
s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has
a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the
generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also
investigated.Comment: 10 page
A Causal Order for Spacetimes with Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves
We recast the tools of ``global causal analysis'' in accord with an approach
to the subject animated by two distinctive features: a thoroughgoing reliance
on order-theoretic concepts, and a utilization of the Vietoris topology for the
space of closed subsets of a compact set. We are led to work with a new causal
relation which we call , and in terms of it we formulate extended
definitions of concepts like causal curve and global hyperbolicity. In
particular we prove that, in a spacetime \M which is free of causal cycles,
one may define a causal curve simply as a compact connected subset of \M
which is linearly ordered by . Our definitions all make sense for
arbitrary metrics (and even for certain metrics which fail to be
invertible in places). Using this feature, we prove for a general metric,
the familiar theorem that the space of causal curves between any two compact
subsets of a globally hyperbolic spacetime is compact. We feel that our
approach, in addition to yielding a more general theorem, simplifies and
clarifies the reasoning involved. Our results have application in a recent
positive energy theorem, and may also prove useful in the study of topology
change. We have tried to make our treatment self-contained by including proofs
of all the facts we use which are not widely available in reference works on
topology and differential geometry.Comment: Two small revisions to accomodate errors brought to our attention by
R.S. Garcia. No change to chief results. 33 page
Gravitational intraction on quantum level and consequences thereof
The notion of gravitational emission as an emission of the same level with
electromagnetic emission is based on the proven fact of existence of electrons
stationary states in its own gravitational field, characterized by
gravitational constantComment: 22 pages, 9 figure
Regular spherical dust spacetimes
Physical (and weak) regularity conditions are used to determine and classify
all the possible types of spherically symmetric dust spacetimes in general
relativity. This work unifies and completes various earlier results. The
junction conditions are described for general non-comoving (and non-null)
surfaces, and the limits of kinematical quantities are given on all comoving
surfaces where there is Darmois matching. We show that an inhomogeneous
generalisation of the Kantowski-Sachs metric may be joined to the
Lemaitre-Tolman-Bondi metric. All the possible spacetimes are explicitly
divided into four groups according to topology, including a group in which the
spatial sections have the topology of a 3-torus. The recollapse conjecture (for
these spacetimes) follows naturally in this approach.Comment: Minor improvements, additional references. Accepted by GR
Classical Integrable 2-dim Models Inspired by SUSY Quantum Mechanics
A class of integrable 2-dim classical systems with integrals of motion of
fourth order in momenta is obtained from the quantum analogues with the help of
deformed SUSY algebra. With similar technique a new class of potentials
connected with Lax method is found which provides the integrability of
corresponding 2-dim hamiltonian systems. In addition, some integrable 2-dim
systems with potentials expressed in elliptic functions are explored.Comment: 19 pages, LaTeX, final version to be published in J.Phys.
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