On the athermal character of structural phase transitions

The significance of thermal fluctuations on nucleation in structural first-order phase transitions has been examined. The prototype case of martensitic transitions has been experimentally investigated by means of acoustic emission techniques. We propose a model based on the mean first-passage time to account for the experimental observations. Our study provides a unified framework to establish the conditions for isothermal and athermal transitions to be observed.Comment: 5 pages, 4 figures, accepted in Phys. Rev. Let

Smectic blue phases: layered systems with high intrinsic curvature

We report on a construction for smectic blue phases, which have quasi-long range smectic translational order as well as three dimensional crystalline order. Our proposed structures fill space by adding layers on top of a minimal surface, introducing either curvature or edge defects as necessary. We find that for the right range of material parameters, the favorable saddle-splay energy of these structures can stabilize them against uniform layered structures. We also consider the nature of curvature frustration between mean curvature and saddle-splay.Comment: 15 pages, 11 figure

Scaling in Plasticity-Induced Cell-Boundary Microstructure: Fragmentation and Rotational Diffusion

We develop a simple computational model for cell boundary evolution in plastic deformation. We study the cell boundary size distribution and cell boundary misorientation distribution that experimentally have been found to have scaling forms that are largely material independent. The cell division acts as a source term in the misorientation distribution which significantly alters the scaling form, giving it a linear slope at small misorientation angles as observed in the experiments. We compare the results of our simulation to two closely related exactly solvable models which exhibit scaling behavior at late times: (i) fragmentation theory and (ii) a random walk in rotation space with a source term. We find that the scaling exponents in our simulation agree with those of the theories, and that the scaling collapses obey the same equations, but that the shape of the scaling functions depend upon the methods used to measure sizes and to weight averages and histograms

Magnetic hysteresis in Ising-like dipole-dipole model

Using zero temperature Monte Carlo simulations we have studied the magnetic hysteresis in a three-dimensional Ising model with nearest neighbor exchange and dipolar interaction. The average magnetization of spins located inside a sphere on a cubic lattice is determined as a function of magnetic field varied periodically. The simulations have justified the appearance of hysteresis and allowed us to have a deeper insight into the series of metastable states developed during this process.Comment: REVTEX, 10 pages including 4 figure

Time Scales for transitions between free energy minima of a hard sphere system

Time scales associated with activated transitions between glassy metastable states of a free energy functional appropriate for a dense hard sphere system are calculated by using a new Monte Carlo method for the local density variables. We calculate the time the system,initially placed in a shallow glassy minimum of the free energy, spends in the neighborhood of this minimum before making a transition to the basin of attarction of another free energy minimum. This time scale is found to increase with the average density. We find a crossover density near which this time scale increases very sharply and becomes longer than the longest times accessible in our simulation. This scale shows no evidence of dependence on sample size.Comment: 25 pages, Revtex, 6 postscript figures. Will appear in Phys Rev E, March 1996 or s

Rate theory for correlated processes: Double-jumps in adatom diffusion

We study the rate of activated motion over multiple barriers, in particular the correlated double-jump of an adatom diffusing on a missing-row reconstructed Platinum (110) surface. We develop a Transition Path Theory, showing that the activation energy is given by the minimum-energy trajectory which succeeds in the double-jump. We explicitly calculate this trajectory within an effective-medium molecular dynamics simulation. A cusp in the acceptance region leads to a sqrt{T} prefactor for the activated rate of double-jumps. Theory and numerical results agree

Cancer Patterns in Karachi Division (1998-1999)

Objective: A minimal cancer incidence data for Karachi, the largest city of Pakistan, is being presented here, for the years 1998-1999. The city has a population of 9,802,134; males 5,261,712 (52.6%) and females 4,540,422 (47.4%); census 19981. Methodology: A predominantly mixed (passive and active) registration system has evolved in Karachi, the data sources being the hospitals within the Karachi Division. The reported/retrieved cancer data sets at the Karachi Cancer Registry are checked, coded, computerised in an analytical format and analysed. Results: The incident cancer cases registered in Karachi, during the 2-year period, 1st January 1998 to 31st December 1999 were analysed. The age-standardised incidence rate (ASR) of cancer, all sites was 132.4/100,000 for the males. Cancer of the lung 10.8%; ASR 17.3 was the most frequently recorded malignancy, followed by oral cavity 10.5%; ASR 13.2 and larynx 5.0%; ASR 7.4. The age-standardised incidence rate (ASR) of cancer, all sites was 133.0/100,000 in the females. Cancer of the breast, 32.0%; ASR 40.7 was the most frequently recorded malignancy, followed by oral cavity 8.1%; ASR 11.7 and gall bladder 3.6%; ASR 5.5. Conclusion: The present data has been calculated with an estimated 15-20% probable under ascertainment. Tobacco-associated cancers in Karachi were responsible for 38.3% of the tumours diagnosed amongst the males. Two principal cancers, breast and oral cavity were responsible for 40.1% of the cancers in females. A rare finding was the high incidence of gall bladder cancer in the females. At present it is difficult to determine whether this indicates a genuine high risk or a selection bias. A continuous process of cancer registration to study the trends in the incidence and an adequate cancer control program are possible and essential for Pakistan and can be based on the pattern being practiced in Karachi

Monte Carlo study of the random-field Ising model

Using a cluster-flipping Monte Carlo algorithm combined with a generalization of the histogram reweighting scheme of Ferrenberg and Swendsen, we have studied the equilibrium properties of the thermal random-field Ising model on a cubic lattice in three dimensions. We have equilibrated systems of LxLxL spins, with values of L up to 32, and for these systems the cluster-flipping method appears to a large extent to overcome the slow equilibration seen in single-spin-flip methods. From the results of our simulations we have extracted values for the critical exponents and the critical temperature and randomness of the model by finite size scaling. For the exponents we find nu = 1.02 +/- 0.06, beta = 0.06 +/- 0.07, gamma = 1.9 +/- 0.2, and gammabar = 2.9 +/- 0.2.Comment: 12 pages, 6 figures, self-expanding uuencoded compressed PostScript fil

Real-space renormalization group for the random-field Ising model

We present real--space renormalization group (RG) calculations of the critical properties of the random--field Ising model on a cubic lattice in three dimensions. We calculate the RG flows in a two--parameter truncation of the Hamiltonian space. As predicted, the transition at finite randomness is controlled by a zero temperature, disordered critical fixed point, and we exhibit the universal crossover trajectory from the pure Ising critical point. We extract scaling fields and critical exponents, and study the distribution of barrier heights between states as a function of length scale.Comment: 12 pages, CU-MSC-757

Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations

We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.Comment: 12 pages plus 2 appended figures, plain TeX, CU-MSC-747