3,142 research outputs found
Cheng Equation: A Revisit Through Symmetry Analysis
The symmetry analysis of the Cheng Equation is performed. The Cheng Equation
is reduced to a first-order equation of either Abel's Equations, the analytic
solution of which is given in terms of special functions. Moreover, for a
particular symmetry the system is reduced to the Riccati Equation or to the
linear nonhomogeneous equation of Euler type. Henceforth, the general solution
of the Cheng Equation with the use of the Lie theory is discussed, as also the
application of Lie symmetries in a generalized Cheng equation.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae
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On fuzzy semi δ – V continuity in fuzzy δ – V topological space
New concepts of fuzzy semi δ – V and fuzzy semi δ – Λ sets were introduced in the work „On fuzzy
semi δ – Λ sets and fuzzy semi δ – V sets V – 6” by the authors (J. Trip. Math. Soc., 6, 81 – 88
(2004)). It was shown that the family of all fuzzy semi δ – V sets forms a fuzzy supra topological space
on X denoted by ( X, FS δV ). The aim of this paper is to introduce the concept of fuzzy semi δ – V
continuity in a fuzzy δ – V topological space. Finally, some properties, preservation theorems, etc., are
studied.Нові поняття нечітких напів δ - V та нечітких напів δ - Λ множин введено у роботі авторів „On fuzzy semi δ - Λ sets and fuzzy semi δ - V sets V - 6" (J. Trip. Math. Soc. - 2004. - 6. - C. 81 - 88). Було показано, що сім'я усіх нечітких напів δ - V множин формує нечіткий супра-топологічний простір в X, що позначається як ( X, FS δ V ). Метою даної статті є введення поняття нестійкої напів δ - V неперервності у нестійкому δ - V топологічному просторі. Також досліджено деякі її властивості, наведено теорему про збереження та інші питання
Continuous loading of S calcium atoms into an optical dipole trap
We demonstrate an efficient scheme for continuous trap loading based upon
spatially selective optical pumping. We discuss the case of S
calcium atoms in an optical dipole trap (ODT), however, similar strategies
should be applicable to a wide range of atomic species. Our starting point is a
reservoir of moderately cold (K) metastable
P-atoms prepared by means of a magneto-optic trap (triplet-MOT). A
focused 532 nm laser beam produces a strongly elongated optical potential for
S-atoms with up to 350 K well depth. A weak focused laser beam
at 430 nm, carefully superimposed upon the ODT beam, selectively pumps the
P-atoms inside the capture volume to the singlet state, where they
are confined by the ODT. The triplet-MOT perpetually refills the capture volume
with P-atoms thus providing a continuous stream of cold atoms into
the ODT at a rate of s. Limited by evaporation loss, in 200 ms we
typically load atoms with an initial radial temperature of 85
K. After terminating the loading we observe evaporation during 50 ms
leaving us with atoms at radial temperatures close to 40 K and a
peak phase space density of . We point out that a
comparable scheme could be employed to load a dipole trap with
P-atoms.Comment: 4 pages, 4 figure
Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models
This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative
(PID) controllers to handle second order processes with time delays (SOPTD).
Previously, similar attempts have been made for pole placement in delay-free systems. The presence
of the time delay term manifests itself as a higher order system with variable number of interlaced
poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement
control. We here report the analytical expressions to constrain the closed loop dominant and nondominant
poles at the desired locations in the complex s-plane, using a third order Pade
approximation for the delay term. However, invariance of the closed loop performance with different
time delay approximation has also been verified using increasing order of Pade, representing a closed
to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being
complex, real or a combination of them modifies the characteristic equation and influences the
achievable stability regions. The effect of different types of non-dominant poles and the
corresponding stability regions are obtained for nine test-bench processes indicating different levels of
open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider
stability region in the design parameter space by using Monte Carlo simulations while uniformly
sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the
design parameter space can then be mapped on to the PID controller parameter space, relating these
two sets of parameters. The widest stability region is then used to find out the most robust solution
which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid
location of the arbitrary shaped stability regions. Various time and frequency domain control
performance parameters are investigated next, as well as their deviations with uncertain process
parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of
the nine test-bench processes. We also report, PID controller tuning rules for the robust stable
solutions using the test-bench processes while also providing computational complexity analysis of
the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different
classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under
its Basic Scientific Research (BSR) schem
Transformation of LQR weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers
This is the author accepted manuscript. The final version is available from Cambridge University Press via the DOI in this record.Linear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller is
used to derive a mapping between continuous and discrete-time inverse optimal equivalence of
proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive
transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic
Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response
to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to
discrete time by establishing a relation between the respective LQR weighting matrices that will produce
similar closed loop response, independent of the chosen sampling time. Simulation examples of
first/second order and first-order integrating processes exhibiting stable/unstable and marginally-stable
open-loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point
and disturbance inputs are compared for different sampling time as fraction of the desired closed-loop
time constant.University Grants Commission (UGC), Government of IndiaESIF ERDF Cornwal
Integrated optical source of polarization entangled photons at 1310 nm
We report the realization of a new polarization entangled photon-pair source
based on a titanium-indiffused waveguide integrated on periodically poled
lithium niobate pumped by a CW laser at . The paired photons are
emitted at the telecom wavelength of within a bandwidth of .
The quantum properties of the pairs are measured using a two-photon coalescence
experiment showing a visibility of 85%. The evaluated source brightness, on the
order of pairs , associated with its
compactness and reliability, demonstrates the source's high potential for
long-distance quantum communication.Comment: There is a typing mistake in the previous version in the visibility
equation. This mistake doesn't change the result
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