Wavelet-Galerkin method for numerical solution of partial differential equation

In recent years wavelets are given much attention in many branches of science and technology due to its comprehensive mathematical power and application potential. The advantage of wavelet techniques over finite difference or element method is well known.The objective of this work is to implementing the Wavelet-Galerkin method for approximating solutions of differential equations. In this paper, we elaborate the wavelet techniques and apply the Galerkin method procedure to analyse one dimensional wave equation as a test problem using fictitious boundary approach. The sections of this thesis will include defining wavelets and their scaling functions.This will give the reader valued insight about wavelets.Following this will be a section defining the Daubechies wavelet and its scaling function. This section comprises some subsection about computing the scaling function and its derivative and integral.The purpose of this section will be to give the reader an understanding how scaling function and its derivative are computed. Next will be a section on multiresolution analysis and its properties. The next section give information about the 2-term connection coefficients. The main focus of this work will be to solve the one dimensional wave equation using fictitious boundary approach and made a comparison between the exact and approximate solution which gives the accuracy and efficiency of this method

Molecular Dipolar Crystals as High Fidelity Quantum Memory for Hybrid Quantum Computing

We study collective excitations of rotational and spin states of an ensemble of polar molecules, which are prepared in a dipolar crystalline phase, as a candidate for a high fidelity quantum memory. While dipolar crystals are formed in the high density limit of cold clouds of polar molecules under 1D and 2D trapping conditions, the crystalline structure protects the molecular qubits from detrimental effects of short range collisions. We calculate the lifetime of the quantum memory by identifying the dominant decoherence mechanisms, and estimate their effects on gate operations, when a molecular ensemble qubit is transferred to a superconducting strip line cavity (circuit QED). In the case rotational excitations coupled by dipole-dipole interactions we identify phonons as the main limitation of the life time of qubits. We study specific setups and conditions, where the coupling to the phonon modes is minimized. Detailed results are presented for a 1D dipolar chain

Dynamic Transition in the Structure of an Energetic Crystal during Chemical Reactions at Shock Front Prior to Detonation

Mechanical stimuli in energetic materials initiate chemical reactions at shock fronts prior to detonation. Shock sensitivity measurements provide widely varying results, and quantum-mechanical calculations are unable to handle systems large enough to describe shock structure. Recent developments in reactive force-field molecular dynamics (ReaxFF-MD) combined with advances in parallel computing have paved the way to accurately simulate reaction pathways along with the structure of shock fronts. Our multimillion-atom ReaxFF-MD simulations of l,3,5-trinitro-l,3,5-triazine (RDX) reveal that detonation is preceded by a transition from a diffuse shock front with well-ordered molecular dipoles behind it to a disordered dipole distribution behind a sharp front

A NWB-based dataset and processing pipeline of human single-neuron activity during a declarative memory task

A challenge for data sharing in systems neuroscience is the multitude of different data formats used. Neurodata Without Borders: Neurophysiology 2.0 (NWB:N) has emerged as a standardized data format for the storage of cellular-level data together with meta-data, stimulus information, and behavior. A key next step to facilitate NWB:N adoption is to provide easy to use processing pipelines to import/export data from/to NWB:N. Here, we present a NWB-formatted dataset of 1863 single neurons recorded from the medial temporal lobes of 59 human subjects undergoing intracranial monitoring while they performed a recognition memory task. We provide code to analyze and export/import stimuli, behavior, and electrophysiological recordings to/from NWB in both MATLAB and Python. The data files are NWB:N compliant, which affords interoperability between programming languages and operating systems. This combined data and code release is a case study for how to utilize NWB:N for human single-neuron recordings and enables easy re-use of this hard-to-obtain data for both teaching and research on the mechanisms of human memory

Genetic analysis of bioactive compounds and antioxidant properties in lettuce (Lactuca sativa)

Leaves of lettuce (Lactuca sativa L.) are the store house of various phytonutrients which have protective properties. Being an important dietary leafy vegetable, it is primarily consumed fresh as salad and in sandwiches, burgers etc. Its beneficial effects are primarily due to the presence of different phytochemicals such as ascorbic acid, carotenoids, polyphenols and fibre which helps in protecting key biological constituents such as lipoproteins, membranes and DNA. However, systematic biochemical nutrient analysis has not been carried out in this important salad vegetable so far. In the present investigation, 36 genotypes were analysed for phytochemicals such as total carotenoids, lycopene, ascorbic acid, total phenolic content, Cupric ion Reducing Antioxidant Capacity (CUPRAC) and Ferric Reducing Antioxidant Power (FRAP). The CUPRAC ranged from 0.05 to 1.98 μmol trolox/g with the highest content in Stem lettuce Angustana, whereas FRAP ranged from 0.06 to 4.70 μmol trolox/g showing, thereby, a considerable variation amongst genotypes. Total phenolics ranged from 41.94 to 501.88 μg gallic acid/g fresh weight. Total carotenoids were found in appreciable amount in Wo Suen (46.13 mg/100g fresh weight), whereas lycopene in New Chicken (17.01 mg/100g fresh weight). Ascorbic content ranged from 1.14 to 3.75 mg/100g fresh weight, whereas per cent moisture ranged from 86.50 (NVRS 10:001818) to 97.32 (Sheetal). Positive correlation was observed between total carotenoids and lycopene, chlorophyll b with chlorophyll a, total chlorophyll with both chlorophyll a and b, FRAP with CUPRAC and phenols with total chlorophyll, chlorophyll a and b. Maximum phenotypic and genotypic coefficients of variance were calculated for FRAP (165.98, 165.98) followed by CUPRAC (122.10,122.10) and lycopene content (83.33, 80.84), respectively. These genotypes can be further utilized for development of multinutrient rich varieties. Regular consumption of lettuce can go a long way in tackling osteoporosis, anemia, and cardiovascular related problems

Quantum Simulations of Extended Hubbard Models with Dipolar Crystals

In this paper we study the realization of lattice models in mixtures of atomic and dipolar molecular quantum gases. We consider a situation where polar molecules form a self-assembled dipolar lattice, in which atoms or molecules of a second species can move and scatter. We describe the system dynamics in a master equation approach in the Brownian motion limit of slow particles and fast phonons, which we find appropriate for our system. In a wide regime of parameters, the reduced dynamics of the particles leads to physical realizations of extended Hubbard models with tuneable long-range interactions mediated by crystal phonons. This extends the notion of quantum simulation of strongly correlated systems with cold atoms and molecules to include phonon-dynamics, where all coupling parameters can be controlled by external fields.Comment: 44 pages, 14 figure

Continuum field description of crack propagation

We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching and fragmentation.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Lett. Additional information can be obtained from http://gershwin.msd.anl.gov/theor

Thermodynamics of Dipolar Chain Systems

The thermodynamics of a quantum system of layers containing perpendicularly oriented dipolar molecules is studied within an oscillator approximation for both bosonic and fermionic species. The system is assumed to be built from chains with one molecule in each layer. We consider the effects of the intralayer repulsion and quantum statistical requirements in systems with more than one chain. Specifically, we consider the case of two chains and solve the problem analytically within the harmonic Hamiltonian approach which is accurate for large dipole moments. The case of three chains is calculated numerically. Our findings indicate that thermodynamic observables, such as the heat capacity, can be used to probe the signatures of the intralayer interaction between chains. This should be relevant for near future experiments on polar molecules with strong dipole moments.Comment: 15 pages, 5 figures, final versio

De Novo Ultrascale Atomistic Simulations On High-End Parallel Supercomputers

We present a de novo hierarchical simulation framework for first-principles based predictive simulations of materials and their validation on high-end parallel supercomputers and geographically distributed clusters. In this framework, high-end chemically reactive and non-reactive molecular dynamics (MD) simulations explore a wide solution space to discover microscopic mechanisms that govern macroscopic material properties, into which highly accurate quantum mechanical (QM) simulations are embedded to validate the discovered mechanisms and quantify the uncertainty of the solution. The framework includes an embedded divide-and-conquer (EDC) algorithmic framework for the design of linear-scaling simulation algorithms with minimal bandwidth complexity and tight error control. The EDC framework also enables adaptive hierarchical simulation with automated model transitioning assisted by graph-based event tracking. A tunable hierarchical cellular decomposition parallelization framework then maps the O(N) EDC algorithms onto Petaflops computers, while achieving performance tunability through a hierarchy of parameterized cell data/computation structures, as well as its implementation using hybrid Grid remote procedure call + message passing + threads programming. High-end computing platforms such as IBM BlueGene/L, SGI Altix 3000 and the NSF TeraGrid provide an excellent test grounds for the framework. On these platforms, we have achieved unprecedented scales of quantum-mechanically accurate and well validated, chemically reactive atomistic simulations--1.06 billion-atom fast reactive force-field MD and 11.8 million-atom (1.04 trillion grid points) quantum-mechanical MD in the framework of the EDC density functional theory on adaptive multigrids--in addition to 134 billion-atom non-reactive space-time multiresolution MD, with the parallel efficiency as high as 0.998 on 65,536 dual-processor BlueGene/L nodes. We have also achieved an automated execution of hierarchical QM/MD simulation on a Grid consisting of 6 supercomputer centers in the US and Japan (in total of 150 thousand processor-hours), in which the number of processors change dynamically on demand and resources are allocated and migrated dynamically in response to faults. Furthermore, performance portability has been demonstrated on a wide range of platforms such as BlueGene/L, Altix 3000, and AMD Opteron-based Linux clusters

Condensed Matter Theory of Dipolar Quantum Gases

Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic, long-range dipolar interactions play a prominent role at the many-body level. In this article we review recent theoretical studies concerning the physics of such systems. Starting from a general discussion on interaction design techniques and microscopic Hamiltonians, we provide a summary of recent work focused on many-body properties of dipolar systems, including: weakly interacting Bose gases, weakly interacting Fermi gases, multilayer systems, strongly interacting dipolar gases and dipolar gases in 1D and quasi-1D geometries. Within each of these topics, purely dipolar effects and connections with experimental realizations are emphasized.Comment: Review article; submitted 09/06/2011. 158 pages, 52 figures. This document is the unedited author's version of a Submitted Work that was subsequently accepted for publication in Chemical Reviews, copyright American Chemical Society after peer review. To access the final edited and published work, a link will be provided soo