57 research outputs found
Transport Equations from Liouville Equations for Fractional Systems
We consider dynamical systems that are described by fractional power of
coordinates and momenta. The fractional powers can be considered as a
convenient way to describe systems in the fractional dimension space. For the
usual space the fractional systems are non-Hamiltonian. Generalized transport
equation is derived from Liouville and Bogoliubov equations for fractional
systems. Fractional generalization of average values and reduced distribution
functions are defined. Hydrodynamic equations for fractional systems are
derived from the generalized transport equation.Comment: 11 pages, LaTe
Fractional Systems and Fractional Bogoliubov Hierarchy Equations
We consider the fractional generalizations of the phase volume, volume
element and Poisson brackets. These generalizations lead us to the fractional
analog of the phase space. We consider systems on this fractional phase space
and fractional analogs of the Hamilton equations. The fractional generalization
of the average value is suggested. The fractional analogs of the Bogoliubov
hierarchy equations are derived from the fractional Liouville equation. We
define the fractional reduced distribution functions. The fractional analog of
the Vlasov equation and the Debye radius are considered.Comment: 12 page
Fractional Liouville and BBGKI Equations
We consider the fractional generalizations of Liouville equation. The
normalization condition, phase volume, and average values are generalized for
fractional case.The interpretation of fractional analog of phase space as a
space with fractal dimension and as a space with fractional measure are
discussed. The fractional analogs of the Hamiltonian systems are considered as
a special class of non-Hamiltonian systems. The fractional generalization of
the reduced distribution functions are suggested. The fractional analogs of the
BBGKI equations are derived from the fractional Liouville equation.Comment: 20 page
Towards Rigorous Derivation of Quantum Kinetic Equations
We develop a rigorous formalism for the description of the evolution of
states of quantum many-particle systems in terms of a one-particle density
operator. For initial states which are specified in terms of a one-particle
density operator the equivalence of the description of the evolution of quantum
many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and
by the Cauchy problem of the generalized quantum kinetic equation together with
a sequence of explicitly defined functionals of a solution of stated kinetic
equation is established in the space of trace class operators. The links of the
specific quantum kinetic equations with the generalized quantum kinetic
equation are discussed.Comment: 25 page
The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems
The Cauchy problem for the von Neumann hierarchy of nonlinear equations is
investigated. One describes the evolution of all possible states of quantum
many-particle systems by the correlation operators. A solution of such
nonlinear equations is constructed in the form of an expansion over particle
clusters whose evolution is described by the corresponding order cumulant
(semi-invariant) of evolution operators for the von Neumann equations. For the
initial data from the space of sequences of trace class operators the existence
of a strong and a weak solution of the Cauchy problem is proved. We discuss the
relationships of this solution both with the -particle statistical
operators, which are solutions of the BBGKY hierarchy, and with the
-particle correlation operators of quantum systems.Comment: 26 page
On Rigorous Derivation of the Enskog Kinetic Equation
We develop a rigorous formalism for the description of the kinetic evolution
of infinitely many hard spheres. On the basis of the kinetic cluster expansions
of cumulants of groups of operators of finitely many hard spheres the nonlinear
kinetic Enskog equation and its generalizations are justified. It is
established that for initial states which are specified in terms of
one-particle distribution functions the description of the evolution by the
Cauchy problem of the BBGKY hierarchy and by the Cauchy problem of the
generalized Enskog kinetic equation together with a sequence of explicitly
defined functionals of a solution of stated kinetic equation is an equivalent.
For the initial-value problem of the generalized Enskog equation the existence
theorem is proved in the space of integrable functions.Comment: 28 page
Addressing the needs of children with disabilities experiencing disaster or terrorism
Purpose of review: This paper reviews the empirical literature on psychosocial factors relating to children with disabilities in the context of disaster or terrorism.
Recent findings: Research indicates individuals with disabilities experience increased exposure to hazards due to existing social disparities and barriers associated with disability status. However, studies on the psychological effects of disaster/terrorism on children with preexisting disabilities are exceedingly few and empirical evidence of the effectiveness of trauma-focused therapies for this population is limited. Secondary adversities, including social stigma and health concerns, also compromise the recovery of these children post-disaster/terrorism. Schools and teachers appear to be particularly important in the recovery of children with disabilities to disaster. Disasters, terrorism, and war all contribute to the incidence of disability, as well as disproportionately affect children with preexisting disabilities.
Summary: Disaster preparedness interventions and societal changes are needed to decrease the disproportionate environmental and social vulnerability of children with disabilities to disaster and terrorism
Some aspects of the Liouville equation in mathematical physics and statistical mechanics
This paper presents some mathematical aspects of Classical Liouville theorem
and we have noted some mathematical theorems about its initial value problem.
Furthermore, we have implied on the formal frame work of Stochastic Liouville
equation (SLE)
Environment: Contributions of Design and Education to the Sustainment of Planet Earth
Any book that aims to deal with issues of sustainable futures will necessarily have a significant focus on environmental sustainability. Historically, concerns over sustainable futures were predominantly focused on the environment, with references going back as far as, for example, the 7th century when legislation was introduced to protect birds in the Farne Islands off the north east coast of England. More recently there has been recognition that sustainable futures depend on complex sets of relationships
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