Kaushik Bhattacharya

Bio: Kaushik Bhattacharya is an academic researcher from California Institute of Technology. The author has contributed to research in topics: Ferroelectricity & Density functional theory. The author has an hindex of 51, co-authored 259 publications receiving 9292 citations. Previous affiliations of Kaushik Bhattacharya include Courant Institute of Mathematical Sciences & New York University.

Microstructure of martensite : why it forms and how it gives rise to the shape-memory effect

Abstract: 1. Introduction 2. Review of Continuum Mechanics 3. Continuum Theory of Crystalline Solids 4. Martensitic Phase Transformation 5. Twinning in Martensite 6. Origin of Microstructure 7. Special Microstructures 8. Analysis of Microstructure 9. The Shape-Memory Effect 10. Thin Films 11. Geometrically Linear Theory 12. Piece-wise Linear Elasticity 13. Polycrystals

Fourier Neural Operator for Parametric Partial Differential Equations

Abstract: The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The Fourier neural operator is the first ML-based method to successfully model turbulent flows with zero-shot super-resolution. It is up to three orders of magnitude faster compared to traditional PDE solvers. Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution.

Domain switching in polycrystalline ferroelectric ceramics.

Abstract: Ferroelectric ceramics are widely used as sensors and actuators for their electro-mechanical properties, and in electronic applications for their dielectric properties. Domain switching – the phenomenon wherein the ferroelectric material changes from one spontaneously polarized state to another under electrical or mechanical loads – is an important attribute of these materials. However, this is a complex collective process in commercially used polycrystalline ceramics that are agglomerations of a very large number of variously oriented grains. As the domains in one grain attempt to switch, they are constrained by the differently oriented neighbouring grains. Here we use a combined theoretical and experimental approach to establish a relation between crystallographic symmetry and the ability of a ferroelectric polycrystalline ceramic to switch. In particular, we show that equiaxed polycrystals of materials that are either tetragonal or rhombohedral cannot switch; yet polycrystals of materials where these two symmetries co-exist can in fact switch.

Crystal symmetry and the reversibility of martensitic transformations.

Abstract: Martensitic transformations are diffusionless, solid-to-solid phase transitions, and have been observed in metals, alloys, ceramics and proteins. They are characterized by a rapid change of crystal structure, accompanied by the development of a rich microstructure. Martensitic transformations can be irreversible, as seen in steels upon quenching, or they can be reversible, such as those observed in shape-memory alloys. In the latter case, the microstructures formed on cooling are easily manipulated by loads and disappear upon reheating. Here, using mathematical theory and numerical simulation, we explain these sharp differences in behaviour on the basis of the change in crystal symmetry during the transition. We find that a necessary condition for reversibility is that the symmetry groups of the parent and product phases be included in a common finite symmetry group. In these cases, the energy barrier to lattice-invariant shear is generically higher than that pertaining to the phase change and, consequently, transformations of this type can occur with virtually no plasticity. Irreversibility is inevitable in all other martensitic transformations, where the energy barrier to plastic deformation (via lattice-invariant shears, as in twinning or slip) is no higher than the barrier to the phase change itself. Various experimental observations confirm the importance of the symmetry of the stable states in determining the macroscopic reversibility of martensitic transformations.

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Plasmonics for extreme light concentration and manipulation.

Abstract: The unprecedented ability of nanometallic (that is, plasmonic) structures to concentrate light into deep-subwavelength volumes has propelled their use in a vast array of nanophotonics technologies and research endeavours. Plasmonic light concentrators can elegantly interface diffraction-limited dielectric optical components with nanophotonic structures. Passive and active plasmonic devices provide new pathways to generate, guide, modulate and detect light with structures that are similar in size to state-of-the-art electronic devices. With the ability to produce highly confined optical fields, the conventional rules for light-matter interactions need to be re-examined, and researchers are venturing into new regimes of optical physics. In this review we will discuss the basic concepts behind plasmonics-enabled light concentration and manipulation, make an attempt to capture the wide range of activities and excitement in this area, and speculate on possible future directions.

Plasmonics beyond the diffraction limit

Abstract: Recent years have seen a rapid expansion of research into nanophotonics based on surface plasmon–polaritons. These electromagnetic waves propagate along metal–dielectric interfaces and can be guided by metallic nanostructures beyond the diffraction limit. This remarkable capability has unique prospects for the design of highly integrated photonic signal-processing systems, nanoresolution optical imaging techniques and sensors. This Review summarizes the basic principles and major achievements of plasmon guiding, and details the current state-of-the-art in subwavelength plasmonic waveguides, passive and active nanoplasmonic components for the generation, manipulation and detection of radiation, and configurations for the nanofocusing of light. Potential future developments and applications of nanophotonic devices and circuits are also discussed, such as in optical signals processing, nanoscale optical devices and near-field microscopy with nanoscale resolution.

Controlling the synthesis and assembly of silver nanostructures for plasmonic applications

Abstract: Coinage metals, such as Au, Ag, and Cu, have been important materials throughout history.1 While in ancient cultures they were admired primarily for their ability to reflect light, their applications have become far more sophisticated with our increased understanding and control of the atomic world. Today, these metals are widely used in electronics, catalysis, and as structural materials, but when they are fashioned into structures with nanometer-sized dimensions, they also become enablers for a completely different set of applications that involve light. These new applications go far beyond merely reflecting light, and have renewed our interest in maneuvering the interactions between metals and light in a field known as plasmonics.2–6 In plasmonics, the metal nanostructures can serve as antennas to convert light into localized electric fields (E-fields) or as waveguides to route light to desired locations with nanometer precision. These applications are made possible through a strong interaction between incident light and free electrons in the nanostructures. With a tight control over the nanostructures in terms of size and shape, light can be effectively manipulated and controlled with unprecedented accuracy.3,7 While many new technologies stand to be realized from plasmonics, with notable examples including superlenses,8 invisible cloaks,9 and quantum computing,10,11 conventional technologies like microprocessors and photovoltaic devices could also be made significantly faster and more efficient with the integration of plasmonic nanostructures.12–15 Of the metals, Ag has probably played the most important role in the development of plasmonics, and its unique properties make it well-suited for most of the next-generation plasmonic technologies.16–18 1.1. What is Plasmonics? Plasmonics is related to the localization, guiding, and manipulation of electromagnetic waves beyond the diffraction limit and down to the nanometer length scale.4,6 The key component of plasmonics is a metal, because it supports surface plasmon polariton modes (indicated as surface plasmons or SPs throughout this review), which are electromagnetic waves coupled to the collective oscillations of free electrons in the metal. While there are a rich variety of plasmonic metal nanostructures, they can be differentiated based on the plasmonic modes they support: localized surface plasmons (LSPs) or propagating surface plasmons (PSPs).5,19 In LSPs, the time-varying electric field associated with the light (Eo) exerts a force on the gas of negatively charged electrons in the conduction band of the metal and drives them to oscillate collectively. At a certain excitation frequency (w), this oscillation will be in resonance with the incident light, resulting in a strong oscillation of the surface electrons, commonly known as a localized surface plasmon resonance (LSPR) mode.20 This phenomenon is illustrated in Figure 1A. Structures that support LSPRs experience a uniform Eo when excited by light as their dimensions are much smaller than the wavelength of the light. Figure 1 Schematic illustration of the two types of plasmonic nanostructures discussed in this article as excited by the electric field (Eo) of incident light with wavevector (k). In (A) the nanostructure is smaller than the wavelength of light and the free electrons ... In contrast, PSPs are supported by structures that have at least one dimension that approaches the excitation wavelength, as shown in Figure 1B.4 In this case, the Eo is not uniform across the structure and other effects must be considered. In such a structure, like a nanowire for example, SPs propagate back and forth between the ends of the structure. This can be described as a Fabry-Perot resonator with resonance condition l=nλsp, where l is the length of the nanowire, n is an integer, and λsp is the wavelength of the PSP mode.21,22 Reflection from the ends of the structure must also be considered, which can change the phase and resonant length. Propagation lengths can be in the tens of micrometers (for nanowires) and the PSP waves can be manipulated by controlling the geometrical parameters of the structure.23