22,406 research outputs found
Matrix Models, Argyres-Douglas singularities and double scaling limits
We construct an N=1 theory with gauge group U(nN) and degree n+1 tree level
superpotential whose matrix model spectral curve develops an A_{n+1}
Argyres-Douglas singularity. We evaluate the coupling constants of the
low-energy U(1)^n theory and show that the large N expansion is singular at the
Argyres-Douglas points. Nevertheless, it is possible to define appropriate
double scaling limits which are conjectured to yield four dimensional
non-critical string theories as proposed by Ferrari. In the Argyres-Douglas
limit the n-cut spectral curve degenerates into a solution with n/2 cuts for
even n and (n+1)/2 cuts for odd n.Comment: 31 pages, 1 figure; the expression of the superpotential has been
corrected and the calculation of the coupling constants of the low-energy
theory has been adde
Bosonic Field Propagators on Algebraic Curves
In this paper we investigate massless scalar field theory on non-degenerate
algebraic curves. The propagator is written in terms of the parameters
appearing in the polynomial defining the curve. This provides an alternative to
the language of theta functions. The main result is a derivation of the third
kind differential normalized in such a way that its periods around the homology
cycles are purely imaginary. All the physical correlation functions of the
scalar fields can be expressed in terms of this object. This paper contains a
detailed analysis of the techniques necessary to study field theories on
algebraic curves. A simple expression of the scalar field propagator is found
in a particular case in which the algebraic curves have internal symmetry
and one of the fields is located at a branch point.Comment: 26 pages, TeX + harvma
Renormalization Group and Conformal Symmetry Breaking in the Chern-Simons Theory Coupled to Matter
The three-dimensional Abelian Chern-Simons theory coupled to a scalar and a
fermionic field of arbitrary charge is considered in order to study conformal
symmetry breakdown and the effective potential stability. We present an
improved effective potential computation based on two-loop calculations and the
renormalization group equation: the later allows us to sum up series of terms
in the effective potential where the power of the logarithms are one, two and
three units smaller than the total power of coupling constants (i.e., leading,
next-to-leading and next-to-next-to-leading logarithms). For the sake of this
calculation we determined the beta function of the
fermion-fermion-scalar-scalar interaction and the anomalous dimension of the
scalar field. We shown that the improved effective potential provides a much
more precise determination of the properties of the theory in the broken phase,
compared to the standard effective potential obtained directly from the loop
calculations. This happens because the region of the parameter space where
dynamical symmetry breaking occurs is drastically reduced by the improvement
discussed here.Comment: 29 pages, 10 figures, 1 tabl
Plug-and-Play Fault Detection and control-reconfiguration for a class of nonlinear large-scale constrained systems
This paper deals with a novel Plug-and-Play (PnP) architecture for the control and monitoring of Large-Scale Systems (LSSs). The proposed approach integrates a distributed Model Predictive Control (MPC) strategy with a distributed Fault Detection (FD) architecture and methodology in a PnP framework. The basic concept is to use the FD scheme as an autonomous decision support system: once a fault is detected, the faulty subsystem can be unplugged to avoid the propagation of the fault in the interconnected LSS. Analogously, once the issue has been solved, the disconnected subsystem can be re-plugged-in. PnP design of local controllers and detectors allow these operations to be performed safely, i.e. without spoiling stability and constraint satisfaction for the whole LSS. The PnP distributed MPC is derived for a class of nonlinear LSSs and an integrated PnP distributed FD architecture is proposed. Simulation results in two paradigmatic examples show the effectiveness and the potential of the general methodology
Renormalization Group Improvement and Dynamical Breaking of Symmetry in a Supersymmetric Chern-Simons-matter Model
In this work, we investigate the consequences of the Renormalization Group
Equation (RGE) in the determination of the effective superpotential and the
study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory
including an Abelian Chern-Simons superfield coupled to N scalar superfields in
(2+1) dimensional spacetime. The classical Lagrangian presents scale
invariance, which is broken by radiative corrections to the effective
superpotential. We calculate the effective superpotential up to two-loops by
using the RGE and the beta functions and anomalous dimensions known in the
literature. We then show how the RGE can be used to improve this calculation,
by summing up properly defined series of leading logs (LL), next-to-leading
logs (NLL) contributions, and so on... We conclude that even if the RGE
improvement procedure can indeed be applied in a supersymmetric model, the
effects of the consideration of the RGE are not so dramatic as it happens in
the non-supersymmetric case.Comment: v4: 11 pages, 1 figure. Version accepted for publication in NP
Water waves overtopping over barriers
A numerical and experimental analysis of the wave overtopping over emerged and submerged structures, is presented. An original model is used in order to simulate three-dimensional free surface flows. The model is based on the numerical solution of the motion equations expressed in an integral form in time-dependent curvilinear coordinates. A non-intrusive and continuous-in-space image analysis technique, which is able to properly identify the free surface even in very shallow waters or breaking waves, is adopted for the experimental tests. Numerical and experimental results are compared, for several wave and water depth conditions
On the critical slowing down exponents of mode coupling theory
A method is provided to compute the parameter exponent yielding the
dynamic exponents of critical slowing down in mode coupling theory. It is
independent from the dynamic approach and based on the formulation of an
effective static field theory. Expressions of in terms of third order
coefficients of the action expansion or, equivalently, in term of six point
cumulants are provided. Applications are reported to a number of mean-field
models: with hard and soft variables and both fully-connected and dilute
interactions. Comparisons with existing results for Potts glass model, ROM,
hard and soft-spin Sherrington-Kirkpatrick and p-spin models are presented.Comment: 4 pages, 1 figur
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