15,026 research outputs found
Mean-Field Limit for a Collision-Avoiding Flocking System and the Time-Asymptotic Flocking Dynamics for the Kinetic Equation
A Collision-Avoiding flocking particle system proposed in [8] is studied in
this paper. The global wellposedness of its corresponding Vlasov-type kinetic
equation is proved. As a corollary of the global stability result, the mean
field limit of the particle system is obtained. Furthermore, the
time-asymptotic flocking behavior of the solution to the kinetic equation is
also derived. The technics used for local wellposedness and stability follow
from similar ideas to those have been used in [3,22,14]. While in order to
extend the local result globally, the main contribution here is to generate a
series of new estimates for this Vlasov type equation, which imply that the
growing of the characteristics can be controlled globally. Further estimates
also show the long time flocking phenomena.Comment: 21 page
Discriminating dark energy models by using the statefinder hierarchy and the growth rate of matter perturbations
We apply the Statefinder hierarchy and the growth rate of matter
perturbations to discriminate modified Chaplygin gas (MCG), generalized
Chaplygin gas (GCG), superfluid Chaplygin gas (SCG), purely kinetic k-essence
(PKK), and CDM model. We plot the evolutional trajectories of these
models in the statefinder plane and in the composite diagnostic plane. We find
that GCG, MCG, SCG, PKK, and CDM can be distinguished well from each
other at the present epoch by using the composite diagnostic . Using other combinations, such as ,
, , and , some of these five dark energy models cannot be distinguished.Comment: 12 pages, 9 figure
Introduction to Holographic Superconductor Models
In the last years it has been shown that some properties of strongly coupled
superconductors can be potentially described by classical general relativity
living in one higher dimension, which is known as holographic superconductors.
This paper gives a quick and introductory overview of some holographic
superconductor models with s-wave, p-wave and d-wave orders in the literature
from point of view of bottom-up, and summarizes some basic properties of these
holographic models in various regimes. The competition and coexistence of these
superconductivity orders are also studied in these superconductor models.Comment: 93 pages, 38 figures, 2 tables; v3: misprints corrected, published
version. arXiv admin note: text overlap with arXiv:1309.5086, arXiv:1007.1981
by other author
P-V criticality in the extended phase space of Gauss-Bonnet black holes in AdS space
We study the criticality and phase transition in the extended phase
space of charged Gauss-Bonnet black holes in anti-de Sitter space, where the
cosmological constant appears as a dynamical pressure of the system and its
conjugate quantity is the thermodynamic volume of the black hole. The black
holes can have a Ricci flat (), spherical (), or hyperbolic ()
horizon. We find that for the Ricci flat and hyperbolic Gauss-Bonnet black
holes, no criticality and phase transition appear, while for the black
holes with a spherical horizon, even when the charge of the black hole is
absent, the criticality and the small black hole/large black hole phase
transition will appear, but it happens only in dimensions; when the
charge does not vanish, the criticality and the small black hole/large
phase transition always appear in dimensions; in the case of , to
have the criticality and the small black hole/large black hole phase
transition, there exists an upper bound for the parameter
, where is the
Gauss-Bonnet coefficient and is the charge of the black hole. We calculate
the critical exponents at the critical point and find that for all cases, they
are the same as those in the van der Waals liquid-gas system.Comment: 23 pages,9 figure
Petrov type I Condition and Dual Fluid Dynamics
Recently Lysov and Strominger [arXiv:1104.5502] showed that imposing Petrov
type I condition on a -dimensional timelike hypersurface embedded in a
-dimensional vacuum Einstein gravity reduces the degrees of freedom in
the extrinsic curvature of the hypersurface to that of a fluid on the
hypersurface, and that the leading-order Einstein constraint equations in terms
of the mean curvature of the embedding give the incompressible Navier-Stokes
equations of the dual fluid. In this paper we show that the non-relativistic
fluid dual to vacuum Einstein gravity does not satisfy the Petrov type I
condition at next order, unless additional constraint such as the irrotational
condition is added. In addition, we show that this procedure can be inversed to
derive the non-relativistic hydrodynamics with higher order corrections through
imposing the Petrov type I condition, and that some second order transport
coefficients can be extracted, but the dual "Petrov type I fluid" does not
match the dual fluid constructed from the geometry of vacuum Einstein gravity
in the non-relativistic limit. We discuss the procedure both on the finite
cutoff surface via the non-relativistic hydrodynamic expansion and on the
highly accelerated surface via the near horizon expansion.Comment: 20 pages, published version, with minor improvement
The evolution of the power law k-essence cosmology
We investigate the evolution of the power law k-essence field in FRWL
spacetime. The autonomous dynamical system and critical points are obtained.
The corresponding cosmological parameters, such as and
, are calculated at these critical points. We find it is possible to
achieve an equation of state crossing through for k-essence field. The
results we obtained indicate that the power law k-essence dark energy model can
be compatible with observations.Comment: 9 pages, 4 figures, some comments are adde
On the minimal affinizations over the quantum affine algebras of type
In this paper, we study the minimal affinizations over the quantum affine
algebras of type by using the theory of cluster algebras. We show that
the -characters of a large family of minimal affinizations of type
satisfy some systems of equations. These equations correspond to mutation
equations of some cluster algebras. Furthermore, we show that the minimal
affinizations in these equations correspond to cluster variables in these
cluster algebras.Comment: arXiv admin note: substantial text overlap with arXiv:1501.00146,
arXiv:1502.0242
Ground state of three qubits coupled to a harmonic oscillator with ultrastrong coupling
We study the Rabi model composed of three qubits coupled to a harmonic
oscillator without involving the rotating-wave approximation. We show that the
ground state of the three-qubit Rabi model can be analytically treated by using
the transformation method, and the transformed ground state agrees well with
the exactly numerical simulation under a wide range of qubit-oscillator
coupling strengths for different detunings. We use the pairwise entanglement to
characterize the ground-state entanglement between any two qubits and show that
it has an approximately quadratic dependence on the qubit-oscillator coupling
strength. Interestingly, we find that there is no qubit-qubit entanglement for
the ground state if the qubit-oscillator coupling strength is large enough.Comment: 5 pages, 2 figures, Physical Review A 88, 045803 (2013
A Disease Diagnosis and Treatment Recommendation System Based on Big Data Mining and Cloud Computing
It is crucial to provide compatible treatment schemes for a disease according
to various symptoms at different stages. However, most classification methods
might be ineffective in accurately classifying a disease that holds the
characteristics of multiple treatment stages, various symptoms, and
multi-pathogenesis. Moreover, there are limited exchanges and cooperative
actions in disease diagnoses and treatments between different departments and
hospitals. Thus, when new diseases occur with atypical symptoms, inexperienced
doctors might have difficulty in identifying them promptly and accurately.
Therefore, to maximize the utilization of the advanced medical technology of
developed hospitals and the rich medical knowledge of experienced doctors, a
Disease Diagnosis and Treatment Recommendation System (DDTRS) is proposed in
this paper. First, to effectively identify disease symptoms more accurately, a
Density-Peaked Clustering Analysis (DPCA) algorithm is introduced for
disease-symptom clustering. In addition, association analyses on
Disease-Diagnosis (D-D) rules and Disease-Treatment (D-T) rules are conducted
by the Apriori algorithm separately. The appropriate diagnosis and treatment
schemes are recommended for patients and inexperienced doctors, even if they
are in a limited therapeutic environment. Moreover, to reach the goals of high
performance and low latency response, we implement a parallel solution for
DDTRS using the Apache Spark cloud platform. Extensive experimental results
demonstrate that the proposed DDTRS realizes disease-symptom clustering
effectively and derives disease treatment recommendations intelligently and
accurately
Enhanced entanglement of two optical modes in optomechanical systems via an optical parametric amplifier
We investigate the effect of a degenerate optical parametric amplifier (OPA)
placed inside an optomechanical cavity on the steady-state entanglement of two
cavity modes, which jointly interact with a mechanical resonator. Two cavity
modes are respectively driven at the red and blue sideband associated with the
mechanical resonator, which generates entanglement between them in the limit of
resolved sideband. The OPA gives rise to single-mode squeezing of the cavity
fields, which results in significant improvement of the two-mode entanglement.
It is found that an optimal nonlinear gain of the OPA exists, depending on the
system temperatures, which yields the maximum entanglement. The improvement is
particularly remarkable for the system at cryogenic temperatures.Comment: 14 pages, 5 figures, to appear in J. Phys.
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