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 $S=1/2$ 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 $Z$ 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 $\tau_{\hbar} \sim (1/\hbar)^{1/\mu}$ with the transport exponent $\mu > 1$ that corresponds to superdiffusive dynamics. We discuss also other possibilities for the breaking time scaling and transition to the logarithmic one $\tau_{\hbar} \sim \ln(1/\hbar)$ with respect to $\hbar$

Optical clock intercomparison with 6×10−196\times 10^{-19} 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 $4.8\times 10^{-17}/\sqrt{\tau}$ for an averaging time $\tau$ in seconds. Synchronous interrogation reveals a quantum projection noise dominated instability of $3.5(2)\times10^{-17}/\sqrt{\tau}$, resulting in a precision of $5.8(3)\times 10^{-19}$ after a single hour of averaging. The ability to measure sub-$10^{-18}$ 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