3,259 research outputs found
Astrophysical fluid simulations of thermally ideal gases with non-constant adiabatic index: numerical implementation
An Equation of State (\textit{EoS}) closes the set of fluid equations.
Although an ideal EoS with a constant \textit{adiabatic index} is the
preferred choice due to its simplistic implementation, many astrophysical fluid
simulations may benefit from a more sophisticated treatment that can account
for diverse chemical processes. Here, we first review the basic thermodynamic
principles of a gas mixture in terms of its thermal and caloric EoS by
including effects like ionization, dissociation as well as temperature
dependent degrees of freedom such as molecular vibrations and rotations. The
formulation is revisited in the context of plasmas that are either in
equilibrium conditions (local thermodynamic- or collisional excitation-
equilibria) or described by non-equilibrium chemistry coupled to optically thin
radiative cooling. We then present a numerical implementation of thermally
ideal gases obeying a more general caloric EoS with non-constant adiabatic
index in Godunov-type numerical schemes.We discuss the necessary modifications
to the Riemann solver and to the conversion between total energy and pressure
(or vice-versa) routinely invoked in Godunov-type schemes. We then present two
different approaches for computing the EoS.The first one employs root-finder
methods and it is best suited for EoS in analytical form. The second one leans
on lookup table and interpolation and results in a more computationally
efficient approach although care must be taken to ensure thermodynamic
consistency. A number of selected benchmarks demonstrate that the employment of
a non-ideal EoS can lead to important differences in the solution when the
temperature range is K where dissociation and ionization occur. The
implementation of selected EoS introduces additional computational costs
although using lookup table methods can significantly reduce the overhead by a
factor .Comment: 17 pages, 10 figures, Accepted for publication in A&
Monopoles and Solitons in Fuzzy Physics
Monopoles and solitons have important topological aspects like quantized
fluxes, winding numbers and curved target spaces. Naive discretizations which
substitute a lattice of points for the underlying manifolds are incapable of
retaining these features in a precise way. We study these problems of discrete
physics and matrix models and discuss mathematically coherent discretizations
of monopoles and solitons using fuzzy physics and noncommutative geometry. A
fuzzy sigma-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov
bound is also put forth.Comment: 17 pages, Latex. Uses amstex, amssymb.Spelling of the name of one
Author corrected. To appear in Commun.Math.Phy
S-Matrix on the Moyal Plane: Locality versus Lorentz Invariance
Twisted quantum field theories on the Groenewold-Moyal plane are known to be
non-local. Despite this non-locality, it is possible to define a generalized
notion of causality. We show that interacting quantum field theories that
involve only couplings between matter fields, or between matter fields and
minimally coupled U(1) gauge fields are causal in this sense. On the other
hand, interactions between matter fields and non-abelian gauge fields violate
this generalized causality. We derive the modified Feynman rules emergent from
these features. They imply that interactions of matter with non-abelian gauge
fields are not Lorentz- and CPT-invariant.Comment: 15 pages, LaTeX, 1 figur
A radiating dyon solution
We give a non-static exact solution of the Einstein-Maxwell equations (with
null fluid), which is a non-static magnetic charge generalization to the
Bonnor-Vaidya solution and describes the gravitational and electromagnetic
fields of a nonrotating massive radiating dyon. In addition, using the
energy-momentum pseudotensors of Einstein and Landau and Lifshitz we obtain the
energy, momentum, and power output of the radiating dyon and find that both
prescriptions give the same result.Comment: 9 pages, LaTe
Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
Recent work [hep-th/0504183,hep-th/0508002] indicates an approach to the
formulation of diffeomorphism invariant quantum field theories (qft's) on the
Groenewold-Moyal (GM) plane. In this approach to the qft's, statistics gets
twisted and the S-matrix in the non-gauge qft's becomes independent of the
noncommutativity parameter theta^{\mu\nu}. Here we show that the noncommutative
algebra has a commutative spacetime algebra as a substructure: the Poincare,
diffeomorphism and gauge groups are based on this algebra in the twisted
approach as is known already from the earlier work of [hep-th/0510059]. It is
natural to base covariant derivatives for gauge and gravity fields as well on
this algebra. Such an approach will in particular introduce no additional gauge
fields as compared to the commutative case and also enable us to treat any
gauge group (and not just U(N)). Then classical gravity and gauge sectors are
the same as those for \theta^{\mu \nu}=0, but their interactions with matter
fields are sensitive to theta^{\mu \nu}. We construct quantum noncommutative
gauge theories (for arbitrary gauge groups) by requiring consistency of twisted
statistics and gauge invariance. In a subsequent paper (whose results are
summarized here), the locality and Lorentz invariance properties of the
S-matrices of these theories will be analyzed, and new non-trivial effects
coming from noncommutativity will be elaborated.
This paper contains further developments of [hep-th/0608138] and a new
formulation based on its approach.Comment: 17 pages, LaTeX, 1 figur
Statistics and UV-IR Mixing with Twisted Poincare Invariance
We elaborate on the role of quantum statistics in twisted Poincare invariant
theories. It is shown that, in order to have twisted Poincare group as the
symmetry of a quantum theory, statistics must be twisted. It is also confirmed
that the removal of UV-IR mixing (in the absence of gauge fields) in such
theories is a natural consequence.Comment: 13 pages, LaTeX; typos correcte
Entropy and Correlation Functions of a Driven Quantum Spin Chain
We present an exact solution for a quantum spin chain driven through its
critical points. Our approach is based on a many-body generalization of the
Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The
resulting nonequilibrium state of the system, while being a pure quantum state,
has local properties of a mixed state characterized by finite entropy density
associated with Kibble-Zurek defects. The entropy, as well as the finite spin
correlation length, are functions of the rate of sweep through the critical
point. We analyze the anisotropic XY spin 1/2 model evolved with a full
many-body evolution operator. With the help of Toeplitz determinants calculus,
we obtain an exact form of correlation functions. The properties of the evolved
system undergo an abrupt change at a certain critical sweep rate, signaling
formation of ordered domains. We link this phenomenon to the behavior of
complex singularities of the Toeplitz generating function.Comment: 16 pgs, 7 fg
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