Effect of Surface Energy Anisotropy on the Stability of Growth Fronts in Multiphase Alloys

Eutectic growth offers a variety of examples for pattern formation which are interesting both for theoreticians as well as experimentalists. One such example of patterns is ternary eutectic colonies which arise as a result of instabilities during growth of two solid phases. Here, in addition to the two major components being exchanged between the solid phases during eutectic growth, there is an impurity component which is rejected by both solid phases. During progress of solidification, there develops a boundary layer of the third impurity component ahead of the solidification front of the two solid phases. Similar to Mullins-Sekerka type instabilities, such a boundary layer tends to make the global solidification envelope unstable to morphological perturbations giving rise to two-phase cells. This phenomenon has been studied numerically in two dimensions for the conditions of directional solidification, by Plapp and Karma (Phys Rev E 66:061608, 2002) using phase-field simulations. While, in the work by Plapp and Karma (Phys Rev E 66:061608, 2002) all interfaces are isotropic, in our presentation, we extend the phase-field model by considering interfacial anisotropy in the solid-solid and solid-liquid interfaces and characterize the role of interfacial anisotropy on the stability of the growth front through phase-field simulations in two dimensions.

Lack of Critical Slowing Down Suggests that Financial Meltdowns Are Not Critical Transitions, yet Rising Variability Could Signal Systemic Risk

Complex systems inspired analysis suggests a hypothesis that financial meltdowns are abrupt critical transitions that occur when the system reaches a tipping point. Theoretical and empirical studies on climatic and ecological dynamical systems have shown that approach to tipping points is preceded by a generic phenomenon called critical slowing down, i.e. an increasingly slow response of the system to perturbations. Therefore, it has been suggested that critical slowing down may be used as an early warning signal of imminent critical transitions. Whether financial markets exhibit critical slowing down prior to meltdowns remains unclear. Here, our analysis reveals that three major US (Dow Jones Index, S&P 500 and NASDAQ) and two European markets (DAX and FTSE) did not exhibit critical slowing down prior to major financial crashes over the last century. However, all markets showed strong trends of rising variability, quantified by time series variance and spectral function at low frequencies, prior to crashes. These results suggest that financial crashes are not critical transitions that occur in the vicinity of a tipping point. Using a simple model, we argue that financial crashes are likely to be stochastic transitions which can occur even when the system is far away from the tipping point. Specifically, we show that a gradually increasing strength of stochastic perturbations may have caused to abrupt transitions in the financial markets. Broadly, our results highlight the importance of stochastically driven abrupt transitions in real world scenarios. Our study offers rising variability as a precursor of financial meltdowns albeit with a limitation that they may signal false alarms.

Ferroelectric origin in one-dimensional undoped ZnO towards high electromechanical response

Ferroelectricity in ZnO is an unlikely physical phenomenon. Here, we show ferroelectricity in undoped 001] ZnO nanorods due to zinc vacancies. Generation of ferroelectricity in a ZnO nanorod effectively increases its piezoelectricity and turns the ZnO nanorod into an ultrahigh-piezoelectric material. Here using piezoelectric force microscopy (PFM), it is observed that increasing the frequency of the AC excitation electric field decreases the effective d(33). Subsequently, the existence of a reversible permanent electric dipole is also found from the P-E hysteresis loop of the ZnO nanorods. Under a high resolution transmission electron microscope (HRTEM), we observe a zinc blende stacking in the wurtzite stacking of a single nanorod along the growth axis. The zinc blende nature of this defect is also supported by the X-ray diffraction (XRD) and Raman spectra. The presence of zinc vacancies in this basal stacking fault modulates p-d hybridization of the ZnO nanorod and produces a magnetic moment through the adjacent oxygen ions. This in turn induces a reversible electric dipole in the non-centrosymmetric nanostructure and is responsible for the ultrahigh-piezoelectric response in these undoped ZnO nanorods. We reveal that this defect engineered ZnO can be considered to be in the competitive class of ultrahigh-piezoelectric nanomaterials for energy harvesting and electromechanical device fabrication.

On the Gaussian Many-to-One X Channel

In this paper, the Gaussian many-to-one X channel (XC), which is a special case of general multiuser XC, is studied. In the Gaussian many-to-one XC, communication links exist between all transmitters and one of the receivers, along with a communication link between each transmitter and its corresponding receiver. As per the XC assumption, transmission of messages is allowed on all the links of the channel. This communication model is different from the corresponding manyto- one interference channel (IC). Transmission strategies, which involve using Gaussian codebooks and treating interference from a subset of transmitters as noise, are formulated for the above channel. Sum-rate is used as the criterion of optimality for evaluating the strategies. Initially, a 3 x 3 many-to-one XC is considered and three transmission strategies are analyzed. The first two strategies are shown to achieve sum-rate capacity under certain channel conditions. For the third strategy, a sum-rate outer bound is derived and the gap between the outer bound and the achieved rate is characterized. These results are later extended to the K x K case. Next, a region in which the many-to-one XC can be operated as a many-to-one IC without the loss of sum-rate is identified. Furthermore, in the above region, it is shown that using Gaussian codebooks and treating interference as noise achieve a rate point that is within K/2 -1 bits from the sum-rate capacity. Subsequently, some implications of the above results to the Gaussian many-to-one IC are discussed. Transmission strategies for the many-to-one IC are formulated, and channel conditions under which the strategies achieve sum-rate capacity are obtained. A region where the sum-rate capacity can be characterized to within K/2 -1 bits is also identified. Finally, the regions where the derived channel conditions are satisfied for each strategy are illustrated for a 3 x 3 many-to-one XC and the corresponding many-to-one IC.

Fuzzy Approach to Rank Global Climate Models

Eleven coupled model intercomparison project 3 based global climate models are evaluated for the case study of Upper Malaprabha catchment, India for precipitation rate. Correlation coefficient, normalised root mean square deviation, and skill score are considered as performance indicators for evaluation in fuzzy environment and assumed to have equal impact on the global climate models. Fuzzy technique for order preference by similarity to an ideal solution is used to rank global climate models. Top three positions are occupied by MIROC3, GFDL2.1 and GISS with relative closeness of 0.7867, 0.7070, and 0.7068. IPSL-CM4, NCAR-PCMI occupied the tenth and eleventh positions with relative closeness of 0.4959 and 0.4562.

One Subject, Two Lands: My Journey in Condensed Matter Physics

This is an account of a professional life in the field that was generally known as solid-state physics when I started working in it; India and the United States of America are the countries in which this life was largely played out. My attempts to understand various things in condensed matter physics, and efforts to put together people and activities in India in this field, are mainly the story.

Integrals of motion for one-dimensional Anderson localized systems

Anderson localization is known to be inevitable in one-dimension for generic disordered models. Since localization leads to Poissonian energy level statistics, we ask if localized systems possess `additional' integrals of motion as well, so as to enhance the analogy with quantum integrable systems. We answer this in the affirmative in the present work. We construct a set of nontrivial integrals of motion for Anderson localized models, in terms of the original creation and annihilation operators. These are found as a power series in the hopping parameter. The recently found Type-1 Hamiltonians, which are known to be quantum integrable in a precise sense, motivate our construction. We note that these models can be viewed as disordered electron models with infinite-range hopping, where a similar series truncates at the linear order. We show that despite the infinite range hopping, all states but one are localized. We also study the conservation laws for the disorder free Aubry-Andre model, where the states are either localized or extended, depending on the strength of a coupling constant. We formulate a specific procedure for averaging over disorder, in order to examine the convergence of the power series. Using this procedure in the Aubry-Andre model, we show that integrals of motion given by our construction are well-defined in localized phase, but not so in the extended phase. Finally, we also obtain the integrals of motion for a model with interactions to lowest order in the interaction.

Efficient simulation and rendering of realistic motion of one-dimensional flexible objects

In gross motion of flexible one-dimensional (1D) objects such as cables, ropes, chains, ribbons and hair, the assumption of constant length is realistic and reasonable. The motion of the object also appears more natural if the motion or disturbance given at one end attenuates along the length of the object. In an earlier work, variational calculus was used to derive natural and length-preserving transformation of planar and spatial curves and implemented for flexible 1D objects discretized with a large number of straight segments. This paper proposes a novel idea to reduce computational effort and enable real-time and realistic simulation of the motion of flexible 1D objects. The key idea is to represent the flexible 1D object as a spline and move the underlying control polygon with much smaller number of segments. To preserve the length of the curve to within a prescribed tolerance as the control polygon is moved, the control polygon is adaptively modified by subdivision and merging. New theoretical results relating the length of the curve and the angle between the adjacent segments of the control polygon are derived for quadratic and cubic splines. Depending on the prescribed tolerance on length error, the theoretical results are used to obtain threshold angles for subdivision and merging. Simulation results for arbitrarily chosen planar and spatial curves whose one end is subjected to generic input motions are provided to illustrate the approach. (C) 2016 Elsevier Ltd. All rights reserved.

The cellular structure of a two-dimensional H2/O2/Ar detonation wave

In this paper, the cellular structure of a two-dimensional detonation wave in a low pressure H2/O2/Ar mixture calculated with a detailed chemical reaction model, high order scheme and high resolution grids is investigated. The regular cellular structure is produced about 1 ms after introducing perturbations in the reaction zone of a steady one-dimensional detonation wave. It is found from the present resolution study that the discrepancies concerning the structure type arising from the coarser grid employed can be resolved using a sufficiently fine grid size of 0.05 mm and below and shows a double-Mach-like strong-type configuration. During the structure evolution process, the structure configuration does not change much in the periods before and after the triple point collision. Through the triple point collision, three regular collision processes are observed and are followed by a quick change to the double-Mach-like configuration. The simulated structure tracks show that there are three different tracks associated with different triple points or the kink on the transverse wave. Comparisons with previous work and experiments indicate the presence of a strong structure for an ordinary detonation.

Microcracks Propagation in One Al/SiCp under Impact Loading

Numerous microcracks propagation in one metal matrix composite, Al/SiCp under impact loading was investigated. The test data was got with a specially designed impact experimental approach. The analysis to the density, nucleating locations and distributions of the microcracks as well as microstructure effects of the original composite was received particular emphasis. The types of microcracks or debonding nucleated in the tested composite were dependent on the stress level and its duration. Distributions of the microcracks were depended on that of microstructures of the tested composite while total number of microcracks in unit area and unit duration, was controlled by the stress levels. Also, why the velocity was much lower than theoretical estimations for elastic solids and why the microcracks propagating velocities increased with the stress levels' increasing in current experiments were analysed and explained.

Comparison Of Shear Banding In Bmgs Due To Thermal-Softening And Free Volume Creation

This paper reports a comparative study of shear banding in BMGs resulting from thermal softening and free volume creation. Firstly, the effects of thermal softening and free volume creation on shear instability are discussed. It is known that thermal softening governs thermal shear banding, hence it is essentially energy related. However, compound free volume creation is the key factor to the other instability, though void-induced softening seems to be the counterpart of thermal softening. So, the driving force for shear instability owing to free volume creation is very different from the thermally assisted one. In particular, long wave perturbations are always unstable owing to compound free volume creation. Therefore, the shear instability resulting from coupled compound free volume creation and thermal softening may start more like that due to free volume creation. Also, the compound free volume creation implies a specific and intrinsic characteristic growth time of shear instability. Finally, the mature shear band width is governed by the corresponding diffusions (thermal or void diffusion) within the band. As a rough guide, the dimensionless numbers: Thermal softening related number B, Deborah number (denoting the relation of instability growth rate owing to compound free volume and loading time) and Lewis number (denoting the competition of different diffusions) show us their relative importance of thermal softening and free volume creation in shear banding. All these results are of particular significance in understanding the mechanism of shear banding in bulk metallic glasses (BMGs).

The vector fields admitting one-parameter spatial symmetry group and their reduction

For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.