462 research outputs found
Thermal stresses in functionally graded hollow sphere due to non-uniform internal heat generation
In this article, the thermal stresses in a hollow thick sphere of functionally graded material subjected to non-uniform internal heat generation are obtained as a function of radius to an exact solution by using the theory of elasticity. Material properties and heat generation are assumed as a function of radius of sphere and Poisson’s ratio as constant. The distribution of thermal stresses for different values of the powers of the module of elasticity and varying power law index of heat generation is studied. The results are illustrated numerically and graphically
Symmetry breaking perturbations and strange attractors
The asymmetrically forced, damped Duffing oscillator is introduced as a
prototype model for analyzing the homoclinic tangle of symmetric dissipative
systems with \textit{symmetry breaking} disturbances. Even a slight fixed
asymmetry in the perturbation may cause a substantial change in the asymptotic
behavior of the system, e.g. transitions from two sided to one sided strange
attractors as the other parameters are varied. Moreover, slight asymmetries may
cause substantial asymmetries in the relative size of the basins of attraction
of the unforced nearly symmetric attracting regions. These changes seems to be
associated with homoclinic bifurcations. Numerical evidence indicates that
\textit{strange attractors} appear near curves corresponding to specific
secondary homoclinic bifurcations. These curves are found using analytical
perturbational tools
Inverse Heat Conduction Problem in a Semi-Infinite Circular Plate and its Thermal Deflection by Quasi-Static Approach
This paper concerns the inverse heat conduction problem in a semi-infinite thin circular plate subjected to an arbitrary known temperature under unsteady condition and the behavior of thermal deflection has been discussed on the outer curved surface with the help of mathematical modeling. The solutions are obtained in an analytical form by using the integral transform technique
Inverse Heat Conduction Problem in a Semi-Infinite Cylinder and its Thermal Stresses by Quasi-Static Approach
The present paper deals with the determination of unknown temperature and thermal stresses on the curved surface of a semi-infinite circular cylinder defined as 0 ≤ r ≤ a , 0 ≤ z ≤ ∞. The circular cylinder is subjected to an arbitrary known temperature under unsteady state condition. Initially, the cylinder is at zero temperature and temperature at the lower surface is held fixed at zero. The governing heat conduction equation has been solved by using the integral transform method. The results are obtained in series form in terms of Bessel’s functions. A mathematical model has been constructed for aluminum material and illustrates the results graphically
Griffiths Effects in Random Heisenberg Antiferromagnetic S=1 Chains
I consider the effects of enforced dimerization on random Heisenberg
antiferromagnetic S=1 chains. I argue for the existence of novel Griffiths
phases characterized by {\em two independent dynamical exponents} that vary
continuously in these phases; one of the exponents controls the density of
spin-1/2 degrees of freedom in the low-energy effective Hamiltonian, while the
other controls the corresponding density of spin-1 degrees of freedom.
Moreover, in one of these Griffiths phases, the system has very different low
temperature behavior in two different parts of the phase which are separated
from each other by a sharply defined crossover line; on one side of this
crossover line, the system `looks' like a S=1 chain at low energies, while on
the other side, it is best thought of as a chain. A strong-disorder RG
analysis makes it possible to analytically obtain detailed information about
the low temperature behavior of physical observables such as the susceptibility
and the specific heat, as well as identify an experimentally accessible
signature of this novel crossover.Comment: 16 pages, two-column PRB format; 5 figure
Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape
Lobe dynamics and escape from a potential well are general frameworks
introduced to study phase space transport in chaotic dynamical systems. While
the former approach studies how regions of phase space are transported by
reducing the flow to a two-dimensional map, the latter approach studies the
phase space structures that lead to critical events by crossing periodic orbit
around saddles. Both of these frameworks require computation with curves
represented by millions of points-computing intersection points between these
curves and area bounded by the segments of these curves-for quantifying the
transport and escape rate. We present a theory for computing these intersection
points and the area bounded between the segments of these curves based on a
classification of the intersection points using equivalence class. We also
present an alternate theory for curves with nontransverse intersections and a
method to increase the density of points on the curves for locating the
intersection points accurately.The numerical implementation of the theory
presented herein is available as an open source software called Lober. We used
this package to demonstrate the application of the theory to lobe dynamics that
arises in fluid mechanics, and rate of escape from a potential well that arises
in ship dynamics.Comment: 33 pages, 17 figure
Spin-3/2 random quantum antiferromagnetic chains
We use a modified perturbative renormalization group approach to study the
random quantum antiferromagnetic spin-3/2 chain. We find that in the case of
rectangular distributions there is a quantum Griffiths phase and we obtain the
dynamical critical exponent as a function of disorder. Only in the case of
extreme disorder, characterized by a power law distribution of exchange
couplings, we find evidence that a random singlet phase could be reached. We
discuss the differences between our results and those obtained by other
approaches.Comment: 4 page
Quantum Breaking Time Scaling in the Superdiffusive Dynamics
We show that the breaking time of quantum-classical correspondence depends on
the type of kinetics and the dominant origin of stickiness. For sticky dynamics
of quantum kicked rotor, when the hierarchical set of islands corresponds to
the accelerator mode, we demonstrate by simulation that the breaking time
scales as with the transport exponent
that corresponds to superdiffusive dynamics. We discuss also other
possibilities for the breaking time scaling and transition to the logarithmic
one with respect to
Optical clock intercomparison with precision in one hour
Improvements in atom-light coherence are foundational to progress in quantum
information science, quantum optics, and precision metrology. Optical atomic
clocks require local oscillators with exceptional optical coherence due to the
challenge of performing spectroscopy on their ultra-narrow linewidth clock
transitions. Advances in laser stabilization have thus enabled rapid progress
in clock precision. A new class of ultrastable lasers based on cryogenic
silicon reference cavities has recently demonstrated the longest optical
coherence times to date. In this work we utilize such a local oscillator, along
with a state-of-the-art frequency comb for coherence transfer, with two Sr
optical lattice clocks to achieve an unprecedented level of clock stability.
Through an anti-synchronous comparison, the fractional instability of both
clocks is assessed to be for an averaging time
in seconds. Synchronous interrogation reveals a quantum projection noise
dominated instability of , resulting in a
precision of after a single hour of averaging. The
ability to measure sub- level frequency shifts in such short
timescales will impact a wide range of applications for clocks in quantum
sensing and fundamental physics. For example, this precision allows one to
resolve the gravitational red shift from a 1 cm elevation change in only 20
minutes
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