412 research outputs found
Solutions of a certain class of fractional differintegral equations
AbstractRecently, several authors demonstrated the usefulness of fractional calculus in obtaining particular solutions of a number of such familiar second-order differential equations as those associated with Gauss, Legendre, Jacobi, Chebyshev, Coulomb, Whittaker, Euler, Hermite, and Weber equations. The main object of this paper is to show how some of the latest contributions on the subject by Tu et al. [1], involving the associated Legendre, Euler, and Hermite equations, can be presented in a unified manner by suitably appealing to a general theorem on particular solutions of a certain class of fractional differintegral equations
Quantum dynamical phase transition in a system with many-body interactions
We introduce a microscopic Hamiltonian model of a two level system with
many-body interactions with an environment whose excitation dynamics is fully
solved within the Keldysh formalism. If a particle starts in one of the states
of the isolated system, the return probability oscillates with the Rabi
frequency . For weak interactions with the environment
we find a slower oscillation whose
amplitude decays with a decoherence rate . However, beyond a finite critical interaction with the environment,
, the decoherence rate becomes
. The oscillation
period diverges showing a \emph{quantum dynamical phase transition}to a Quantum
Zeno phase.Comment: 5 pages, 3 figures, minor changes, fig.2 modified, added reference
Development of a reduced biodiesel surrogate fuel model for multi- dimensional CFD simulations
This work reports the development of a reduced biodiesel surrogate fuel model for multi-dimensional CFD simulations. The model is derived using an integrated kinetic mechanism reduction scheme and the final chemistry comprises only 83 species. The model is first validated in zero-dimensional (0-D) chemical kinetic calculations under a wide range of auto-ignition and jet-stirred reactor (JSR) conditions. The computed ignition delays (ID) and species profiles are in well agreement with those of the detailed model. Besides, the experimental species profiles of rapeseed methyl ester (RME) oxidation in a JSR are also reasonably reproduced. Subsequently, the fidelity of the model is further assessed in two-dimensional (2-D) CFD simulations of a constant-volume combustion vessel with respect to the experimental results of soy-methyl ester (SME) combustion. Comparisons
of the computations with the experimental data reveal that ID, lift-off lengths (LOL) and soot volume fractions
are reasonably well replicated by the model. Successively, the applicability of the reduced model to serve as a
universal surrogate model for other biodiesel feed-stocks, such as palm-methyl ester (PME) and sunflower-methyl
ester (SFME), is investigated in both 0-D and 2-D simulations. The compositions of the reduced model are varied according to the saturation/unsaturation levels in each fuel. In this work, it is demonstrated that the reduced model can potentially be used to predict the reactivity of biodiesel feed-stocks with low degree of saturation (≤30%) in both kinetic and CFD spray simulations
Notes on Non-Critical Superstrings in Various Dimensions
We study non-critical superstrings propagating in dimensional
Minkowski space or equivalently, superstrings propagating on the
two-dimensional Euclidean black hole tensored with d-dimensional Minkowski
space. We point out a subtlety in the construction of supersymmetric theories
in these backgrounds, and explain how this does not allow a consistent
geometric interpretation in terms of fields propagating on a cigar-like
spacetime. We explain the global symmetries of the various theories by using
their description as the near horizon geometry of wrapped NS5-brane
configurations. In the six-dimensional theory, we present a CFT description of
the four-dimensional moduli space and the global O(3) symmetry. The worldsheet
action invariant under this symmetry contains both the N=2 sine-Liouville
interaction and the cigar metric, thereby providing an example where the two
interactions are naturally present in the same worldsheet lagrangian already at
the non-dynamical level.Comment: 33 pages, harvma
A Mathematical Model of Liver Cell Aggregation In Vitro
The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work
Statefinder and Om Diagnostics for Interacting New Holographic Dark Energy Model and Generalized Second Law of Thermodynamics
In this work, we have considered that the flat FRW universe is filled with
the mixture of dark matter and the new holographic dark energy. If there is an
interaction, we have investigated the natures of deceleration parameter,
statefinder and diagnostics. We have examined the validity of the first
and generalized second laws of thermodynamics under these interactions on the
event as well as apparent horizon. It has been observed that the first law is
violated on the event horizon. However, the generalized second law is valid
throughout the evolution of the universe enveloped by the apparent horizon.
When the event horizon is considered as the enveloping horizon, the generalized
second law is found to break down excepting at late stage of the universe.Comment: 9 pages, 13 figure
Measurements of the observed cross sections for exclusive light hadrons containing at , 3.650 and 3.6648 GeV
By analyzing the data sets of 17.3, 6.5 and 1.0 pb taken,
respectively, at , 3.650 and 3.6648 GeV with the BES-II
detector at the BEPC collider, we measure the observed cross sections for
, , ,
and at the three energy
points. Based on these cross sections we set the upper limits on the observed
cross sections and the branching fractions for decay into these
final states at 90% C.L..Comment: 7 pages, 2 figure
Partial wave analysis of J/\psi \to \gamma \phi \phi
Using events collected in the BESII detector, the
radiative decay is
studied. The invariant mass distribution exhibits a near-threshold
enhancement that peaks around 2.24 GeV/.
A partial wave analysis shows that the structure is dominated by a
state () with a mass of
GeV/ and a width of GeV/. The
product branching fraction is: .Comment: 11 pages, 4 figures. corrected proof for journa
Direct Measurements of Absolute Branching Fractions for D0 and D+ Inclusive Semimuonic Decays
By analyzing about 33 data sample collected at and around 3.773
GeV with the BES-II detector at the BEPC collider, we directly measure the
branching fractions for the neutral and charged inclusive semimuonic decays
to be and , and determine the ratio of the two branching
fractions to be
Measurements of the observed cross sections for exclusive light hadron production in e^+e^- annihilation at \sqrt{s}= 3.773 and 3.650 GeV
By analyzing the data sets of 17.3 pb taken at GeV
and 6.5 pb taken at GeV with the BESII detector at the
BEPC collider, we have measured the observed cross sections for 12 exclusive
light hadron final states produced in annihilation at the two energy
points. We have also set the upper limits on the observed cross sections and
the branching fractions for decay to these final states at 90%
C.L.Comment: 8 pages, 5 figur
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