127 research outputs found
Some new results in state space decoupling of multivariable systems. I. A link between geometric approach and matrix methods
Adaptive defuzzification for fuzzy systems modeling
We propose a new parameterized method for the defuzzification process based on the simple M-SLIDE transformation. We develop a computationally efficient algorithm for learning the relevant parameter as well as providing a computationally simple scheme for doing the defuzzification step in the fuzzy logic controllers. The M-SLIDE method results in a particularly simple linear form of the algorithm for learning the parameter which can be used both off- and on-line
Some new results in state space decoupling of multivariable systems. II. Extensions to decoupling of systems with and output feedback decoupling
Universal Holographic Chiral Dynamics in an External Magnetic Field
In this work we further extend the investigation of holographic gauge
theories in external magnetic fields, continuing earlier work. We study the
phenomenon of magnetic catalysis of mass generation in 1+3 and 1+2 dimensions,
using D3/D7- and D3/D5-brane systems, respectively. We obtain the low energy
effective actions of the corresponding pseudo Goldstone bosons and study their
dispersion relations. The D3/D7 system exhibits the usual
Gell-Mann--Oakes--Renner (GMOR) relation and a relativistic dispersion
relation, while the D3/D5 system exhibits a quadratic non-relativistic
dispersion relation and a modified linear GMOR relation. The low energy
effective action of the D3/D5 system is related to that describing magnon
excitations in a ferromagnet. We also study properties of general Dp/Dq systems
in an external magnetic field and verify the universality of the magnetic
catalysis of dynamical symmetry breaking.Comment: 41 pages, 11 figures, references adde
Critical Exponents from AdS/CFT with Flavor
We use the AdS/CFT correspondence to study the thermodynamics of massive N=2
supersymmetric hypermultiplet flavor fields coupled to N=4 supersymmetric
SU(Nc) Yang-Mills theory, formulated on curved four-manifolds, in the limits of
large Nc and large 't Hooft coupling. The gravitational duals are probe
D-branes in global thermal AdS. These D-branes may undergo a topology-changing
transition in the bulk. The D-brane embeddings near the point of the topology
change exhibit a scaling symmetry. The associated scaling exponents can be
either real- or complex-valued. Which regime applies depends on the
dimensionality of a collapsing submanifold in the critical embedding. When the
scaling exponents are complex-valued, a first-order transition associated with
the flavor fields appears in the dual field theory. Real scaling exponents are
expected to be associated with a continuous transition in the dual field
theory. For one example with real exponents, the D7-brane, we study the
transition in detail. We find two field theory observables that diverge at the
critical point, and we compute the associated critical exponents. We also
present analytic and numerical evidence that the transition expresses itself in
the meson spectrum as a non-analyticity at the critical point. We argue that
the transition we study is a true phase transition only when the 't Hooft
coupling is strictly infinite.Comment: 31 pages, 21 eps files in 12 figures; v2 added one reference and one
footnote, version published in JHE
Holographic Flavor Transport in Arbitrary Constant Background Fields
We use gauge-gravity duality to compute a new transport coefficient
associated with a number Nf of massive N=2 supersymmetric hypermultiplet fields
propagating through an N=4 SU(Nc) super-Yang-Mills theory plasma in the limits
of large Nc and large 't Hooft coupling, with Nf << Nc. We introduce a baryon
number density as well as arbitrary constant electric and magnetic fields,
generalizing previous calculations by including a magnetic field with a
component parallel to the electric field. We can thus compute all components of
the conductivity tensor associated with transport of baryon number charge,
including a component never before calculated in gauge-gravity duality. We also
compute the contribution that the flavor degrees of freedom make to the
stress-energy tensor, which exhibits divergences associated with the rates of
energy and momentum loss of the flavor degrees of freedom. We discuss two
currents that are free from these divergences, one of which becomes anomalous
when the magnetic field has a component parallel to the electric field and
hence may be related to recent study of charge transport in the presence of
anomalies.Comment: 27 page
Dynamics of the chiral phase transition from AdS/CFT duality
We use Lorentzian signature AdS/CFT duality to study a first order phase
transition in strongly coupled gauge theories which is akin to the chiral phase
transition in QCD. We discuss the relation between the latent heat and the
energy (suitably defined) of the component of a D-brane which lies behind the
horizon at the critical temperature. A numerical simulation of a dynamical
phase transition in an expanding, cooling Quark-Gluon plasma produced in a
relativistic collision is carried out.Comment: 30 pages, 5 figure
Scaling limit of the one-dimensional attractive Hubbard model: The non-half-filled band case
The scaling limit of the less than half filled attractive Hubbard chain is
studied. This is a continuum limit in which the particle number per lattice
site, n, is kept finite (0<n<1) while adjusting the interaction and bandwidth
in a such way that there is a finite mass gap. We construct this limit both for
the spectrum and the secular equations describing the excitations. We find,
that similarly to the half filled case, the limiting model has a massive and a
massless sector. The structure of the massive sector is closely analogous to
that of the half filled band and consequently to the chiral invariant SU(2)
Gross-Neveu (CGN) model. The structure of the massless sector differs from that
of the half filled band case: the excitations are of particle and hole type,
however they are not uniquely defined. The energy and the momentum of this
sector exhibits a tower structure corresponding to a conformal field theory
with c=1 and SU(2)xSU(2) symmetry. The energy-momentum spectrum and the zero
temperature free energy of the states with finite density coincides with that
of the half filled case supporting the identification of the limiting model
with the SU(2) symmetric CGN theory.Comment: Latex, 28 page
Flavor-symmetry Breaking with Charged Probes
We discuss the recombination of brane/anti-brane pairs carrying brane
charge in . These configurations are dual to co-dimension one
defects in the super-Yang-Mills description. Due to their
charge, these defects are actually domain walls in the dual gauge theory,
interpolating between vacua of different gauge symmetry. A pair of unjoined
defects each carry localized dimensional fermions and possess a global
flavor symmetry while the recombined brane/anti-brane pairs
exhibit only a diagonal U(N). We study the thermodynamics of this
flavor-symmetry breaking under the influence of external magnetic field.Comment: 21 pages, 10 figure
Sum rules, plasma frequencies and Hall phenomenology in holographic plasmas
We study the AC optical and hall conductivities of Dp/Dq-branes intersections
in the probe approximation and use sum-rules to study various associated
transport coefficients. We determine that the presence of massive fundamental
matter, as compared to massless fundamental matter described holographically by
a theory with no dimensional defects, reduces the plasma frequency. We further
show that this is not the case when the brane intersections include defects. We
discuss in detail how to implement correctly the regularization of retarded
Green's functions so that the dispersion relations are satisfied and the low
energy behaviour of the system is physically realistic.Comment: 25 pages, 5 figures. v2.minor changes, published versio
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