168 research outputs found
Quantized representation of some nonlinear integrable evolution equations on the soliton sector
The Hirota algorithm for solving several integrable nonlinear evolution
equations is suggestive of a simple quantized representation of these equations
and their soliton solutions over a Fock space of bosons or of fermions. The
classical nonlinear wave equation becomes a nonlinear equation for an operator.
The solution of this equation is constructed through the operator analog of the
Hirota transformation. The classical N-solitons solution is the expectation
value of the solution operator in an N-particle state in the Fock space.Comment: 12 page
Cepheid Calibration of the Peak Brightness of SNe Ia -- IX. SN 1989B in NGC 3627
(Abridged) Repeated imaging observations have been made of NGC 3627 with the
HST in 1997/98, over an interval of 58 days. Images were obtained on 12 epochs
in the F555W band and on five epochs in the F814W band. The galaxy hosted the
prototypical, `Branch normal', type Ia supernova SN 1989B. A total of 83
variables have been found, of which 68 are definite Cepheid variables with
periods ranging from 75 days to 3.85 days. The de-reddened distance modulus is
determined to be (m-M)_0= 30.22+/-0.12 (internal uncertainty) using a subset of
the Cepheid data whose reddening and error parameters are secure.
The photometric data of Wells et al. (1994), combined with the Cepheid data
for NGC 3627 give M_B(max)= -19.36+/-0.18 and M_V(max)= -19.34+/-0.16 for SN
1989B. Combined with the previous six calibrations in this program, plus two
additional calibrations determined by others gives the mean absolute magnitudes
at maximum of = -19.48+/-0.07 and = -19.48 +/-0.07 for `Branch
normal' SNe Ia at this interim stage in the calibration program.
The second parameter correlations of M(max) of blue SNe Ia with decay rate,
color at maximum, and Hubble type are re-investigated. The dependence of
on decay rate is non-linear, showing a minimum for decay rates between
1.0< Delta m_15 <1.6. Magnitudes corrected for decay rate show no dependence on
Hubble type, but a dependence on color remains. Correcting both the fiducial
sample of 34 SNe Ia with decay-rate data and the current 8 calibrating SNe Ia
for the correlation with decay rate as well as color gives H_0= 60+/-2
(internal) km/s/Mpc, in both B and V. The same value to within 4% is obtained
if only the SNe Ia in spirals (without second parameter corrections) are
considered.Comment: 32 pages (with 7 tables and 14 figures) LaTeX, uses emulateapj.sty; a
full-resolution version with complete figs. 4 and 5 is available at
http://www.astro.unibas.ch/cosmology/papers.html ; accepted for publication
in Ap
Recasting Navier–Stokes equations
Classical Navier-Stokes equations fail to describe some flows in both the
compressible and incompressible configurations. In this article, we propose a
new methodology based on transforming the fluid mass velocity vector field to
obtain a new class of continuum models. We uncover a class of continuum models
which we call the re-casted Navier-Stokes. They naturally exhibit the physics
of previously proposed models by different authors to substitute the original
Navier-Stokes equations. The new models unlike the conventional Navier-Stokes
appear as more complete forms of mass diffusion type continuum flow equations.
They also form systematically a class of thermo-mechanically consistent
hydrodynamic equations via the original equations. The plane wave analysis is
performed to check their linear stability under small perturbations, which
confirms that all re-casted models are spatially and temporally stable like
their classical counterpart. We then use the Rayleigh-Brillouin scattering
experiments to demonstrate that the re-casted equations may be better suited
for explaining some of the experimental data where original Navier-Stokes fail
Asymptotic models for the generation of internal waves by a moving ship, and the dead-water phenomenon
This paper deals with the dead-water phenomenon, which occurs when a ship
sails in a stratified fluid, and experiences an important drag due to waves
below the surface. More generally, we study the generation of internal waves by
a disturbance moving at constant speed on top of two layers of fluids of
different densities. Starting from the full Euler equations, we present several
nonlinear asymptotic models, in the long wave regime. These models are
rigorously justified by consistency or convergence results. A careful
theoretical and numerical analysis is then provided, in order to predict the
behavior of the flow and in which situations the dead-water effect appears.Comment: To appear in Nonlinearit
Diffuse-interface model for rapid phase transformations in nonequilibrium systems
A thermodynamic approach to rapid phase transformations within a diffuse
interface in a binary system is developed. Assuming an extended set of
independent thermodynamic variables formed by the union of the classic set of
slow variables and the space of fast variables, we introduce finiteness of the
heat and solute diffusive propagation at the finite speed of the interface
advancing. To describe the transformation within the diffuse interface, we use
the phase-field model which allows us to follow the steep but smooth change of
phases within the width of diffuse interface. The governing equations of the
phase-field model are derived for the hyperbolic model, model with memory, and
for a model of nonlinear evolution of transformation within the
diffuse-interface. The consistency of the model is proved by the condition of
positive entropy production and by the outcomes of the fluctuation-dissipation
theorem. A comparison with the existing sharp-interface and diffuse-interface
versions of the model is given.Comment: 15 pages, regular article submitted to Physical Review
A New Nonlinear Liquid Drop Model. Clusters as Solitons on The Nuclear Surface
By introducing in the hydrodynamic model, i.e. in the hydrodynamic equations
and the corresponding boundary conditions, the higher order terms in the
deviation of the shape, we obtain in the second order the Korteweg de Vries
equation (KdV). The same equation is obtained by introducing in the liquid drop
model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms
in the second order. The KdV equation has the cnoidal waves as steady-state
solutions. These waves could describe the small anharmonic vibrations of
spherical nuclei up to the solitary waves. The solitons could describe the
preformation of clusters on the nuclear surface. We apply this nonlinear liquid
drop model to the alpha formation in heavy nuclei. We find an additional
minimum in the total energy of such systems, corresponding to the solitons as
clusters on the nuclear surface. By introducing the shell effects we choose
this minimum to be degenerated with the ground state. The spectroscopic factor
is given by the ratio of the square amplitudes in the two minima.Comment: 27 pages, LateX, 8 figures, Submitted J. Phys. G: Nucl. Part. Phys.,
PACS: 23.60.+e, 21.60.Gx, 24.30.-v, 25.70.e
Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I
We propose an algorithmic procedure i) to study the ``distance'' between an
integrable PDE and any discretization of it, in the small lattice spacing
epsilon regime, and, at the same time, ii) to test the (asymptotic)
integrability properties of such discretization. This method should provide, in
particular, useful and concrete informations on how good is any numerical
scheme used to integrate a given integrable PDE. The procedure, illustrated on
a fairly general 10-parameter family of discretizations of the nonlinear
Schroedinger equation, consists of the following three steps: i) the
construction of the continuous multiscale expansion of a generic solution of
the discrete system at all orders in epsilon, following the Degasperis -
Manakov - Santini procedure; ii) the application, to such expansion, of the
Degasperis - Procesi (DP) integrability test, to test the asymptotic
integrability properties of the discrete system and its ``distance'' from its
continuous limit; iii) the use of the main output of the DP test to construct
infinitely many approximate symmetries and constants of motion of the discrete
system, through novel and simple formulas.Comment: 34 pages, no figur
The Hubble Constant: A Summary of the HST Program for the Luminosity Calibration of Type Ia Supernovae by Means of Cepheids
This is the fifth and final summary paper of our 15 year program using the
Hubble Space Telescope (HST) to determine the Hubble constant using Type Ia
supernovae, calibrated with Cepheid variables in nearby galaxies that hosted
them. Several developments not contemplated at the start of the program in 1990
have made it necessary to put the summary on H_0 on a broader basis than
originally thought, making four preparatory papers necessary. The new Cepheid
distances of the subset of 10 galaxies, which were hosts of normal SNeIa, give
weighted mean luminosities in B, V, and I at maximum light of -19.49, -19.46,
and -19.22, respectively. These calibrate the adopted SNeIa Hubble diagram from
Paper III to give a global value of H_0 = 62.3 +/- 1.3 (random) +/- 5.0
(systematic). Local values of H_0 between 4.4 and 30 Mpc from Cepheids, SNeIa,
21cm-line widths, and the tip of the red-giant branch (TRGB) all agree within
5% of our global value. This agreement of H_0 on all scales from 4 - 200 Mpc
finds its most obvious explanation in the smoothing effect of vacuum energy on
the otherwise lumpy gravitational field due to the non-uniform distribution of
the local galaxies. The physical methods of time delay of gravitational lenses
and the Sunyaev-Zeldovich effect are consistent (but with large errors) with
our global value. The present result is also not in contradiction with existing
analyses of CMB data, because they either lead to wide error margins of H_0 or
depend on the choice of unwarrented priors that couple the value of H_0 with a
number of otherwise free parameters in the CMB acoustic waves. Our value of H_0
is 14% smaller than the value of H_0 found by Freedman et al. (2001) because
our independent Cepheid distances to the six SNeIa-calibrating galaxies used in
that analysis average 0.35mag larger than those used earlier.Comment: 52 pages, 9 figures, 8 tables, accepted for publication in Ap
Time-Fractional KdV Equation: Formulation and Solution using Variational Methods
In this work, the semi-inverse method has been used to derive the Lagrangian
of the Korteweg-de Vries (KdV) equation. Then, the time operator of the
Lagrangian of the KdV equation has been transformed into fractional domain in
terms of the left-Riemann-Liouville fractional differential operator. The
variational of the functional of this Lagrangian leads neatly to Euler-Lagrange
equation. Via Agrawal's method, one can easily derive the time-fractional KdV
equation from this Euler-Lagrange equation. Remarkably, the time-fractional
term in the resulting KdV equation is obtained in Riesz fractional derivative
in a direct manner. As a second step, the derived time-fractional KdV equation
is solved using He's variational-iteration method. The calculations are carried
out using initial condition depends on the nonlinear and dispersion
coefficients of the KdV equation. We remark that more pronounced effects and
deeper insight into the formation and properties of the resulting solitary wave
by additionally considering the fractional order derivative beside the
nonlinearity and dispersion terms.Comment: The paper has been rewritten, 12 pages, 3 figure
On peaked solitary waves of Degasperis - Procesi equation
The Degasperis - Procesi (DP) equation describing the propagation of shallow
water waves contains a physical parameter , and it is well-known that
the DP equation admits solitary waves with a peaked crest when . In
this article, we illustrate, for the first time, that the DP equation admits
peaked solitary waves even when . This is helpful to enrich our
knowledge and deepen our understandings about peaked solitary waves of the DP
equation.Comment: 11 pages, 3 figures, accepted by Science China - Physics, Mechanics &
Astronom
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