7,229 research outputs found
Extended Quintessence with non-minimally coupled phantom scalar field
We investigate evolutional paths of an extended quintessence with a
non-minimally coupled phantom scalar field to the Ricci curvature. The
dynamical system methods are used to investigate typical regimes of dynamics at
the late time. We demonstrate that there are two generic types of evolutional
scenarios which approach the attractor (a focus or a node type critical point)
in the phase space: the quasi-oscillatory and monotonic trajectories approach
to the attractor which represents the FRW model with the cosmological constant.
We demonstrate that dynamical system admits invariant two-dimensional
submanifold and discussion that which cosmological scenario is realized depends
on behavior of the system on the phase plane . We formulate
simple conditions on the value of coupling constant for which
trajectories tend to the focus in the phase plane and hence damping
oscillations around the mysterious value . We describe this condition in
terms of slow-roll parameters calculated at the critical point. We discover
that the generic trajectories in the focus-attractor scenario come from the
unstable node. It is also investigated the exact form of the parametrization of
the equation of state parameter (directly determined from dynamics)
which assumes a different form for both scenarios.Comment: revtex4, 15 pages, 9 figures; (v2) published versio
Scalar field cosmology in the energy phase-space -- unified description of dynamics
In this letter we apply dynamical system methods to study all evolutional
paths admissible for all initial conditions of the FRW cosmological model with
a non-minimally coupled to gravity scalar field and a barotropic fluid. We
choose "energy variables" as phase variables. We reduce dynamics to a
3-dimensional dynamical system for an arbitrary potential of the scalar field
in the phase space variables. After postulating the potential parameter
as a function of (defined as ) we reduce whole
dynamics to a 3-dimensional dynamical system and study evolutional paths
leading to current accelerating expansion. If we restrict the form of the
potential then we will obtain a 2-dimensional dynamical system. We use the
dynamical system approach to find a new generic quintessence scenario of
approaching to the de Sitter attractor which appears only for the case of
non-vanishing coupling constant.Comment: revtex4, 16 pages, 3 figs; (v2) refs. added, published versio
Narrowing Frontiers of Efficiency with Evolutional Communication Rules and Cell Separation
In the framework of Membrane Computing, several efficient solutions to computationally
hard problems have been given. To find new borderlines between families of
P systems that can solve them and the ones that cannot is an important way to tackle the
P versus NP problem. Adding syntactic and/or semantic ingredients can mean passing
from non-efficiency to presumably efficiency. Here, we try to get narrow frontiers, setting
the stage to adapt efficient solutions from a family of P systems to another one. In order
to do that, a solution to the SAT problem is given by means of a family of tissue P systems
with evolutional symport/antiport rules and cell separation with the restriction that both
the left-hand side and the right-hand side of the rules have at most two objects.Ministerio de EconomÃa y Competitividad TIN2017-89842-PNational Natural Science Foundation of China No 6132010600
Cosmological zoo -- accelerating models with dark energy
ecent observations of type Ia supernovae indicate that the Universe is in an
accelerating phase of expansion. The fundamental quest in theoretical cosmology
is to identify the origin of this phenomenon. In principle there are two
possibilities: 1) the presence of matter which violates the strong energy
condition (a substantial form of dark energy), 2) modified Friedmann equations
(Cardassian models -- a non-substantial form of dark matter). We classify all
these models in terms of 2-dimensional dynamical systems of the Newtonian type.
We search for generic properties of the models. It is achieved with the help of
Peixoto's theorem for dynamical system on the Poincar{\'e} sphere. We find that
the notion of structural stability can be useful to distinguish the generic
cases of evolutional paths with acceleration. We find that, while the
CDM models and phantom models are typical accelerating models, the
cosmological models with bouncing phase are non-generic in the space of all
planar dynamical systems. We derive the universal shape of potential function
which gives rise to presently accelerating models. Our results show explicitly
the advantages of using a potential function (instead of the equation of state)
to probe the origin of the present acceleration. We argue that simplicity and
genericity are the best guide in understanding our Universe and its
acceleration.Comment: RevTeX4, 23 pages, 10 figure
Existence of the solution to a nonlocal-in-time evolutional problem
This work is devoted to the study of a nonlocal-in-time evolutional problem
for the first order differential equation in Banach space. Our primary
approach, although stems from the convenient technique based on the reduction
of a nonlocal problem to its classical initial value analogue, uses more
advanced analysis. That is a validation of the correctness in definition of the
general solution representation via the Dunford-Cauchy formula. Such approach
allows us to reduce the given existence problem to the problem of locating
zeros of a certain entire function. It results in the necessary and sufficient
conditions for the existence of a generalized (mild) solution to the given
nonlocal problem. Aside of that we also present new sufficient conditions which
in the majority of cases generalize existing results.Comment: This article is an extended translation of the part of Dmytro
Sytnyk's PhD Thesi
Clinical-evolutional particularities of the cryoglobulinemic vasculitis in the case of a patient diagnosed with hepatitis C virus in the predialitic phase
Hepatitis C virus (HCV) represents a fundamental issue for public health, with long term evolution and the gradual appearance of several complications and associated pathologies. One of these pathologies is represented by cryoglobulinemic vasculitis, a disorder characterized by the appearance in the patient’s serum of the cryoglobulins, which typically precipitate at temperatures below normal body temperature (37°C) and dissolve again if the serum is heated. Here, we describe the case of a patient diagnosed with HCV that, during the evolution of the hepatic disease, developed a form of cryoglobulinemic vasculitis. The connection between the vasculitis and the hepatic disorder was revealed following treatment with interferon, with the temporary remission of both pathologies and subsequent relapse at the end of the 12 months of treatment, the patient becoming a non-responder. The particularity of the case is represented by both the severity of the vasculitic disease from its onset and the deterioration of renal function up to the predialitic phase, a situation not typical of the evolution of cryoglobulinemia. Taking into account the hepatic disorder, the inevitable evolution towards cirrhosis, and the risk of developing the hepatocellular carcinoma, close monitoring is necessary
Dynamical complexity of the Brans-Dicke cosmology
The dynamics of the Brans-Dicke theory with a quadratic scalar field
potential function and barotropic matter is investigated. The dynamical system
methods are used to reveal complexity of dynamical evolution in homogeneous and
isotropic cosmological models. The structure of phase space crucially depends
on the parameter of the theory as well as barotropic
matter index . In our analysis these parameters are treated as
bifurcation parameters. We found sets of values of these parameters which lead
to generic evolutional scenarios. We show that in isotropic and homogeneous
models in the Brans-Dicke theory with a quadratic potential function the de
Sitter state appears naturally. Stability conditions of this state are fully
investigated. It is shown that these models can explain accelerated expansion
of the Universe without the assumption of the substantial form of dark matter
and dark energy. The Poincare construction of compactified phase space with a
circle at infinity is used to show that phase space trajectories in a physical
region can be equipped with a structure of a vector field on nontrivial
topological closed space. For we show new types of
early and late time evolution leading from the anti-de Sitter to the de Sitter
state through an asymmetric bounce. In the theory without a ghost we find
bouncing solutions and the coexistence of the bounces and the singularity.
Following the Peixoto theorem some conclusions about structural stability are
drawn.Comment: 34 pages, 14 figs; (v2) 36 pages, 16 figs, refs. added, JCAP (in
press
Paths of Friedmann-Robertson-Walker brane models
Dynamics of brane-world models of dark energy is reviewed. We demonstrate
that simple dark energy brane models can be represented as 2-dimensional
dynamical systems of a Newtonian type. Hence a fictitious particle moving in a
potential well characterizes the model. We investigate the dynamics of the
brane models using methods of dynamical systems. The simple brane-world models
can be successfully unified within a single scheme -- an ensemble of brane dark
energy models. We characterize generic models of this ensemble as well as
exceptional ones using the notion of structural stability (instability). Then
due to the Peixoto theorem we can characterize the class of generic brane
models. We show that global dynamics of the generic brane models of dark energy
is topologically equivalent to the concordance CDM model. We also
demonstrate that the bouncing models or models in which acceleration of the
universe is only transient phenomenon are non-generic (or exceptional cases) in
the ensemble. We argue that the adequate brane model of dark energy should be a
generic case in the ensemble of FRW dynamical systems on the plane.Comment: revtex4, 14 pages, 11 figures; (v2) title changed, published versio
- …