9,447 research outputs found
Does a prestellar core always become protostellar? Tracing the evolution of cores from the prestellar to protostellar phase
Recently, a subset of starless cores whose thermal Jeans mass is apparently
overwhelmed by the mass of the core has been identified, e.g., the core {\small
L183}. In literature, massive cores such as this one are often referred to as
"super-Jeans cores". As starless cores are perhaps on the cusp of forming
stars, a study of their dynamics will improve our understanding of the
transition from the prestellar to the protostellar phase. In the present work
we use non-magnetic polytropes belonging originally to the family of the
Isothermal sphere. For the purpose, perturbations were applied to individual
polytropes, first by replacing the isothermal gas with a gas that was cold near
the centre of the polytrope and relatively warm in the outer regions, and
second, through a slight compression of the polytrope by raising the external
confining pressure. Using this latter configuration we identify thermodynamic
conditions under which a core is likely to remain starless. In fact, we also
argue that the attribute "super-Jeans" is subjective and that these cores do
not formally violate the Jeans stability criterion. On the basis of our test
results we suggest that gas temperature in a star-forming cloud is crucial
towards the formation and evolution of a core. Simulations in this work were
performed using the particle-based Smoothed Particle Hydrodynamics algorithm.
However, to establish numerical convergence of the results we suggest similar
tests with a grid-scheme, such as the Adaptive mesh refinement.Comment: 14 pages, 24 figures and 1 table; To appear in Monthly Notices of the
Royal Astronomical Societ
The solution of the quantum T-system for arbitrary boundary
We solve the quantum version of the -system by use of quantum
networks. The system is interpreted as a particular set of mutations of a
suitable (infinite-rank) quantum cluster algebra, and Laurent positivity
follows from our solution. As an application we re-derive the corresponding
quantum network solution to the quantum -system and generalize it to
the fully non-commutative case. We give the relation between the quantum
-system and the quantum lattice Liouville equation, which is the quantized
-system.Comment: 24 pages, 18 figure
Discrete integrable systems, positivity, and continued fraction rearrangements
In this review article, we present a unified approach to solving discrete,
integrable, possibly non-commutative, dynamical systems, including the - and
-systems based on . The initial data of the systems are seen as cluster
variables in a suitable cluster algebra, and may evolve by local mutations. We
show that the solutions are always expressed as Laurent polynomials of the
initial data with non-negative integer coefficients. This is done by
reformulating the mutations of initial data as local rearrangements of
continued fractions generating some particular solutions, that preserve
manifest positivity. We also show how these techniques apply as well to
non-commutative settings.Comment: 24 pages, 2 figure
Elliptic Genera and the Landau-Ginzburg Approach to N=2 Orbifolds
We compute the elliptic genera of orbifolds associated with
super--conformal theories which admit a Landau-Ginzburg description. The
identification of the elliptic genera of the macroscopic Landau-Ginzburg
orbifolds with those of the corresponding microscopic orbifolds further
supports the conjectured identification of these theories. For
Kazama-Suzuki models the orbifolds are associated with certain \IZ_p
subgroups of the various coset factors. Based on our approach we also
conjecture the existence of "-type" variants of these theories, their
elliptic genera and the corresponding Landau-Ginzburg potentials.Comment: 27p, uses harvmac (b). negligible change: suppression of the
draftmod
The 3-dimensional oscillon equation
On a bounded three-dimensional smooth domain, we consider the generalized
oscillon equation with Dirichlet boundary conditions, with time-dependent
damping and time-dependent squared speed of propagation. Under structural
assumptions on the damping and the speed of propagation, which include the
relevant physical case of reheating phase of inflation, we establish the
existence of a pullback global attractor of optimal regularity, and
finite-dimensionality of the kernel sections
Time-Dependent Attractor for the Oscillon Equation
We investigate the asymptotic behavior of the nonautonomous evolution problem
generated by the Klein-Gordon equation in an expanding background, in one space
dimension with periodic boundary conditions, with a nonlinear potential of
arbitrary polynomial growth. After constructing a suitable dynamical framework
to deal with the explicit time dependence of the energy of the solution, we
establish the existence of a regular, time-dependent global attractor. The
sections of the attractor at given times have finite fractal dimension.Comment: to appear in Discrete and Continuous Dynamical System
Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
The sums of components of the ground states of the O(1) loop model on a
cylinder or of the XXZ quantum spin chain at Delta=-1/2 (of size L) are
expressed in terms of combinatorial numbers. The methods include the
introduction of spectral parameters and the use of integrability, a mapping
from size L to L+1, and knot-theoretic skein relations.Comment: final version to be publishe
Inhomogeneous loop models with open boundaries
We consider the crossing and non-crossing O(1) dense loop models on a
semi-infinite strip, with inhomogeneities (spectral parameters) that preserve
the integrability. We compute the components of the ground state vector and
obtain a closed expression for their sum, in the form of Pfaffian and
determinantal formulas.Comment: 42 pages, 31 figures, minor corrections, references correcte
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