3,467 research outputs found
A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen Values
We consider a PT Symmetric Partner to Khare Mandal's recently proposed
non-Hermitian potential with complex eigen values. Our potential is
Quasi-Exactly solvable and is shown to possess only real eigen values.Comment: 10 page
Linear-quadratic stochastic differential games for distributed parameter systems
A linear-quadratic differential game with infinite dimensional state space is considered. The system state is affected by disturbance and both players have access to different measurements. Optimal linear strategies for the pursuer and the evader, when they exist, are explicitly determined
Parameter estimation of electricity spot models from futures prices
We consider a slight perturbation of the Schwartz-Smith model for the electricity futures prices and the resulting modified spot model. Using the martingale property of the modified price under the risk neutral measure, we derive the arbitrage free model for the spot and futures prices. We estimate the parameters of the model by the method of maximum likelihood using the Kalman filter's estimate of the unobservable state variables, coupled with the usual statistical techniques. The main advantage of the new model is that it avoids the inclusion of artificial noise to the observation equation for the implementation of Kalman filter. The extra noise is build in within the model in an arbitrage free setting
PT-symmetric square well and the associated SUSY hierarchies
The PT-symmetric square well problem is considered in a SUSY framework. When
the coupling strength lies below the critical value
where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY
partner potentials, depicting an unbroken SUSY situation and reducing to the
family of -like potentials in the limit. For above
, there is a rich diversity of SUSY hierarchies, including
some with PT-symmetry breaking and some with partial PT-symmetry restoration.Comment: LaTeX, 18 pages, no figure; broken PT-symmetry case added (Sec. 6
A new approach to particle based smoothed marginal MAP
We present here a new method of finding the MAP state estimator from the weighted particles representation of marginal smoother distribution. This is in contrast to the usual practice, where the particle with the highest weight is selected as the MAP, although the latter is not necessarily the most probable state estimate. The method developed here uses only particles with corresponding filtering and smoothing weights. We apply this estimator for finding the unknown initial state of a dynamical system and addressing the parameter estimation problem
Fiscal decentralisation and gender responsive budgeting in South Africa: An appraisal.
Fiscal decentralisation ; Gender ; South Africa
Morse potential and its relationship with the Coulomb in a position-dependent mass background
We provide some explicit examples wherein the Schr\"odinger equation for the
Morse potential remains exactly solvable in a position-dependent mass
background. Furthermore, we show how in such a context, the map from the full
line to the half line may convert an exactly
solvable Morse potential into an exactly solvable Coulomb one. This generalizes
a well-known property of constant-mass problems.Comment: 9 pages, no figure; final published versio
Nucleation of a stable solid from melt in the presence of multiple metastable intermediate phases: Wetting, Ostwald step rule and vanishing polymorphs
In many systems, nucleation of a stable solid may occur in the presence of
other (often more than one) metastable phases. These may be polymorphic solids
or even liquid phases. In such cases, nucleation of the solid phase from the
melt may be facilitated by the metastable phase because the latter can "wet"
the interface between the parent and the daughter phases, even though there may
be no signature of the existence of metastable phase in the thermodynamic
properties of the parent liquid and the stable solid phase. Straightforward
application of classical nucleation theory (CNT) is flawed here as it
overestimates the nucleation barrier since surface tension is overestimated (by
neglecting the metastable phases of intermediate order) while the thermodynamic
free energy gap between daughter and parent phases remains unchanged. In this
work we discuss a density functional theory (DFT) based statistical mechanical
approach to explore and quantify such facilitation. We construct a simple order
parameter dependent free energy surface that we then use in DFT to calculate
(i) the order parameter profile, (ii) the overall nucleation free energy
barrier and (iii) the surface tension between the parent liquid and the
metastable solid and also parent liquid and stable solid phases. The theory
indeed finds that the nucleation free energy barrier can decrease significantly
in the presence of wetting. This approach can provide a microscopic explanation
of Ostwald step rule and the well-known phenomenon of "disappearing polymorphs"
that depends on temperature and other thermodynamic conditions. Theory reveals
a diverse scenario for phase transformation kinetics some of which may be
explored via modern nanoscopic synthetic methods
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