Session J26: Focus Session: What is Computational Physics?

Aneesur Rahman Prize for Computational Physics Lecture: Photonic Crystals and Genetic Algorithms: Adventures of a Computational Physicist

I will review some of our work in the computation of photonic crystals, focusing on our discovery of the photonic band gap in diamond structures. I will also describe our conception of the cut-and-paste genetic algorithm in materials discovery structure search and discuss applications of the algorithm from early studies of atomic clusters geometries to more recent applications for structures of surfaces, interfaces, nanowires, and bulk crystals.   

Computational Science as a Data and Compute Intensive Environment: How do we Prepare the Future for it?

Much has been said about the data- and compute-driven transformations that science is undergoing. Much has also been said about the impacts this transformation will have in society, impacts that are not limited to science professionals. But not much been said about the transformations that will have to take place for this impact on society to be positive. This talk will ask if we know enough about what the multiple institutions that educate society's members should be doing to serve the new needs, and discuss some challenging questions that could inform future action.   

New Approaches for Microscopic Hydrodynamics for the Study of Fluid-Structure Interactions Subject to Thermal Fluctuations

Many problems in fluid mechanics involve the interaction of a hydrodynamic flow with an elastic structure. Recent advances in biology and engineering further motivate such studies at small length and time scales. At such scales traditional continuum mechanics descriptions must be augmented to take into account microscopic phenomena, such as spontaneous thermal fluctuations. This presents a variety of challenges both in formulating appropriate physical models and in computational simulation. In the context of fluid-structure interactions, additional challenges arise from the often subtle interplay between elastic mechanics, hydrodynamic coupling, and thermal fluctuations. In this talk, we present a set of new approaches which address central mathematical, physical, and computational issues for how to incorporate in the description of such fluid-structure interactions thermal fluctuations. We also address important numerical issues in the approximation of the resulting stochastic partial differential equations. We also discuss results for specific illustrative applications including studies of polymeric fluids, vesicles, gels, and lipid bilayer membranes.   

Extending the Flux Operator with the Husimi Projection

A common tool among physics in the transport community is the probability flux operator, but connecting this operator to measurement has not received much attention. We have extended the definition of flux by using coherent states, rendering it both measurable and infinitely more useful. For instance, we can use our extended definition to study closed systems and the classical dynamics of individual quantum states, and then connect these dynamics to resonant states interacting with an environment. This analytical technique, based on semi-classics, brings new tools to bear on wavefunction analysis and visualization   

Finite Element Modeling of Open Domain Quantum Scattering

We study quantum scattering in the open domain in 2D using the finite element method. We solve the Schr\"odinger equation in a circular region using an arbitrary triangular mesh with a plane wave source and an arbitrary (finite) scattering potential. We employ perfectly matched layers (PML) around the region of interest to simplify the derivative Cauchy BCs to Dirichlet BCs. With PML, fewer resources are needed to account for the open domain without going to the asymptotic region as is usually done, while obtaining the ``near-field'' evanescent solutions when they are present. The scattering total cross-section, the differential cross-section, and the phase shifts can be determined by performing a partial wave analysis on the computed solution. Examples of this technique and results on multi-component, spin dependent scattering for spintronics will be presented.   

Solution of a Schroedinger equation containing a general non local potential

The non locality is given by an integral kernel K(r,r') that is general. We solve the corresponding Lippmann-Schwinger integral equation a) by expanding the wave function into a Fourier series (Galerkin method), and b) by a spectral method involving Chebyshev polynomials (CP). We apply them to the case of the much used Perey-Buck kernel [1], and find that, by using 50 sine functions, method a) requires an hour of computing time, while method b) using 50 CP's takes less than one second and is precise to 1:10$^{5}$. Previously the spectral method could be applied only to a kernel of rank 1, representing for example the knock-on exchange process [2], but with our new procedure we will be able to compare relatively easily the effect of several types of non localities [3]. \\[4pt] [1] F. G. Perey and B. Buck, Nucl. Phys. \textbf{A 32}, 353 (1962). \newline [2] G.H.,Rawitscher, S.Y. Kang, and I. Koltracht, J. Chem. Phys., \textbf{118},9149-9157, (2003). \newline [3] M. I. Jaghoub, M. F. Hassan and G. H. Rawitscher, Phys. Rev. \textbf{C} 84,034618(2011).   

Accurate and fast numerical solution of Poisson's equation for arbitrary, space-filling convex Voronoi polyhedra: near-field corrections revisited

We present an accurate and rapid solution of Poisson's equation for space-filling, arbitrarily-shaped, convex Voronoi polyhedra (VP); the method is O(N), where N is the number of distinct VP representing the system. In effect, we resolve the longstanding problem of fast but accurate numerical solution of the near-field corrections (NFC), contributions to each VP potential from nearby VP -- typically involving multipole-type conditionally-convergent sums, or fast Fourier transforms. Our method avoids all ill-convergent sums, is simple, accurate, efficient, and works generally, i.e., for periodic solids, molecules, or systems with disorder or imperfections. We demonstrate the method's practicality by numerical calculations compared to exactly solvable models.   

Sonoluminescence and Vacuum Radiation

Sonoluminescence is the generation of light from sound. Our goal is to understand why a bubble trapped in water could generate light from sound. In our work we investigate the contribution of the dynamical Casimir effect to this phenomenon. In previous work researchers have approach this problem as a semi static Casimir effect and have not been able to show a significant contribution of the Casimir effect to sonoluminescence. In our approach, we treat the surface of the bubble as a highly reflecting surface, thus, the electric field of the zero-point modes at the surface is zero. Thus, when the bubble collapses the zero-point modes inside and outside are disturbed. Since the dynamics of zero-point mode fields obey Maxwell equations we can simulate their dynamics using programs like Mathematica. We study the radiation of the excited zero-point mode field.   

Second harmonic generation in three-dimensional metamaterials based on homogeneous centrosymmetric spheres

The theory of second harmonic generation in three-dimensional metamaterials consisting of arbitrary distributions of spheres made of centrosymmetric materials is developed by means of the multiple scattering method. The electromagnetic field at both the fundamental frequency and second harmonic, as well as the scattering cross section, are calculated in a series of particular cases such as a single metallic sphere, two metallic spheres, chains of metallic spheres, and other periodic distributions of the metallic spheres. It is shown that the linear and nonlinear optical response of all ensembles of metallic spheres is strongly influenced by the excitation of surface plasmon-polariton resonances. The physical origin for such a phenomenon has also been analyzed. A new class of SHG devices made of such materials is anticipated.   

Characterizing the frequency response curve of large rooms in the short and long time regimes

Room acoustics can be modeled by real Gaussian statistics, corresponding to randomized ray trajectories and characterized for instance by the reverberation time T60 (free field to decay by 60 decibels) which is independent of position or source point in a room. In his 1954 paper, Manfred Schroeder found universal statistical features of the steady state frequency response curve of large rooms, based upon the assumption of Gaussian probability distributions of the pressure. For example, he found the standard deviation from the mean level is 11 decibels for any concert hall, regardless of the shape of the room or its T60, within reasonable limits. Using semi-classical and numerical methods, we find non-universal (room dependent) corrections to Schroeder's universal results for the statistics of the frequency response curve. Along with corrections to the steady-state frequency response, we present the behavior of the frequency response curve for short to intermediate times.