4,505 research outputs found
Critical Boundary Sine-Gordon Revisited
We revisit the exact solution of the two space-time dimensional quantum field
theory of a free massless boson with a periodic boundary interaction and
self-dual period. We analyze the model by using a mapping to free fermions with
a boundary mass term originally suggested in ref.[22]. We find that the entire
SL(2,C) family of boundary states of a single boson are boundary sine-Gordon
states and we derive a simple explicit expression for the boundary state in
fermion variables and as a function of sine-Gordon coupling constants. We use
this expression to compute the partition function. We observe that the solution
of the model has a strong-weak coupling generalization of T-duality. We then
examine a class of recently discovered conformal boundary states for compact
bosons with radii which are rational numbers times the self-dual radius. These
have simple expression in fermion variables. We postulate sine-Gordon-like
field theories with discrete gauge symmmetries for which they are the
appropriate boundary states.Comment: 33 pages, 1 figure, references added, typos correcte
Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review
Immersed boundary methods for computing confined fluid and plasma flows in
complex geometries are reviewed. The mathematical principle of the volume
penalization technique is described and simple examples for imposing Dirichlet
and Neumann boundary conditions in one dimension are given. Applications for
fluid and plasma turbulence in two and three space dimensions illustrate the
applicability and the efficiency of the method in computing flows in complex
geometries, for example in toroidal geometries with asymmetric poloidal
cross-sections.Comment: in Journal of Plasma Physics, 201
The determinant of the Dirichlet-to-Neumann map for surfaces with boundary
For any orientable compact surface with boundary, we compute the regularized
determinant of the Dirichlet-to-Neumann (DN) map in terms of particular values
of dynamical zeta functions by using natural uniformizations, one due to
Mazzeo-Taylor, the other to Osgood-Phillips-Sarnak. We also relate in any
dimension the DN map for the Yamabe operator to the scattering operator for a
conformally compact related problem by using uniformization.Comment: 16 page
On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations
The present paper deals with the numerical solution of the incompressible
Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods
for discretization in space. For DG methods applied to the dual splitting
projection method, instabilities have recently been reported that occur for
coarse spatial resolutions and small time step sizes. By means of numerical
investigation we give evidence that these instabilities are related to the
discontinuous Galerkin formulation of the velocity divergence term and the
pressure gradient term that couple velocity and pressure. Integration by parts
of these terms with a suitable definition of boundary conditions is required in
order to obtain a stable and robust method. Since the intermediate velocity
field does not fulfill the boundary conditions prescribed for the velocity, a
consistent boundary condition is derived from the convective step of the dual
splitting scheme to ensure high-order accuracy with respect to the temporal
discretization. This new formulation is stable in the limit of small time steps
for both equal-order and mixed-order polynomial approximations. Although the
dual splitting scheme itself includes inf-sup stabilizing contributions, we
demonstrate that spurious pressure oscillations appear for equal-order
polynomials and small time steps highlighting the necessity to consider inf-sup
stability explicitly.Comment: 31 page
Left-Right Entanglement Entropy of Dp-branes
We compute the left-right entanglement entropy for Dp-branes in string
theory. We employ the CFT approach to string theory Dp-branes, in particular,
its presentation as coherent states of the closed string sector. The
entanglement entropy is computed as the von Neumann entropy for a density
matrix resulting from integration over the left-moving degrees of freedom. We
discuss various crucial ambiguities related to sums over spin structures and
argue that different choices capture different physics; however, we advance a
themodynamic argument that seems to favor a particular choice of replica. We
also consider Dp branes on compact dimensions and verify that the effects of
T-duality act covariantly on the Dp brane entanglement entropy. We find that
generically the left-right entanglement entropy provides a suitable
generalization of boundary entropy and of the D-brane tension.Comment: 20 pages, 3 figures. v2: A thermodynamic argument favoring a
particular treatment of spin structures is advanced; one figure improved and
references adde
Finite temperature Casimir effect for massive scalar field in spacetime with extra dimensions
We compute the finite temperature Casimir energy for massive scalar field
with general curvature coupling subject to Dirichlet or Neumann boundary
conditions on the walls of a closed cylinder with arbitrary cross section,
located in a background spacetime of the form ,
where is the -dimensional Minkowski spacetime and
is an -dimensional internal manifold. The Casimir energy is
regularized using the criteria that it should vanish in the infinite mass
limit. The Casimir force acting on a piston moving freely inside the closed
cylinder is derived and it is shown that it is independent of the
regularization procedure. By letting one of the chambers of the cylinder
divided by the piston to be infinitely long, we obtain the Casimir force acting
on two parallel plates embedded in the cylinder. It is shown that if both the
plates assume Dirichlet or Neumann boundary conditions, the strength of the
Casimir force is reduced by the increase in mass. Under certain conditions, the
passage from massless to massive will change the nature of the force from long
range to short range. Other properties of the Casimir force such as its sign,
its behavior at low and high temperature, and its behavior at small and large
plate separations, are found to be similar to the massless case. Explicit exact
formulas and asymptotic behaviors of the Casimir force at different limits are
derived. The Casimir force when one plate assumes Dirichlet boundary condition
and one plate assumes Neumann boundary condition is also derived and shown to
be repulsive.Comment: 28 pages, 4 figure
Mode summation approach to Casimir effect between two objects
In this paper, we explore the TGTG formula from the perspective of mode
summation approach. Both scalar fields and electromagnetic fields are
considered. In this approach, one has to first solve the equation of motion to
find a wave basis for each object. The two T's in the TGTG formula are
T-matrices representing the Lippmann-Schwinger T-operators, one for each of the
objects. The two G's in the TGTG formula are the translation matrices, relating
the wave basis of an object to the wave basis of the other object. After
discussing the general theory, we apply the prescription to derive the explicit
formulas for the Casimir energies for the sphere-sphere, sphere-plane,
cylinder-cylinder and cylinder-plane interactions. First the T-matrices for a
plane, a sphere and a cylinder are derived for the following cases: the object
is imposed with general Robin boundary conditions; the object is
semitransparent; and the object is magnetodielectric. Then the operator
approach is used to derive the translation matrices. From these, the explicit
TGTG formula for each of the scenarios can be written down. Besides summarizing
all the TGTG formulas that have been derived so far, we also provide the TGTG
formulas for some scenarios that have not been considered before.Comment: 42 page
Boundary State from Ellwood Invariants
Boundary states are given by appropriate linear combinations of Ishibashi
states. Starting from any OSFT solution and assuming Ellwood conjecture we show
that every coefficient of such a linear combination is given by an Ellwood
invariant, computed in a slightly modified theory where it does not trivially
vanish by the on-shell condition. Unlike the previous construction of
Kiermaier, Okawa and Zwiebach, ours is linear in the string field, it is
manifestly gauge invariant and it is also suitable for solutions known only
numerically. The correct boundary state is readily reproduced in the case of
known analytic solutions and, as an example, we compute the energy momentum
tensor of the rolling tachyon from the generalized invariants of the
corresponding solution. We also compute the energy density profile of
Siegel-gauge multiple lump solutions and show that, as the level increases, it
correctly approaches a sum of delta functions. This provides a gauge invariant
way of computing the separations between the lower dimensional D-branes.Comment: v2: 63 pages, 14 figures. Major improvements in section 2. Version
published in JHE
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