HyperBlazer.net - Research
http://www.hyperblazer.net/taxonomy/term/11/0
enNote about links to papers
http://www.hyperblazer.net/node/11
<p>The links to papers below connect you to a DOI reference, which will in turn link to the abstract for each article. If you are browsing from an institution which allows electronic access to the article, you can access the PDF directly. If you're interested in the research described, but can't access the articles, please contact the principle investigator for the project who will be happy to provide you with more information.</p>
ResearchMon, 21 Jan 2008 09:29:31 -070011 at http://www.hyperblazer.netFermion Dynamics from a Classical Hamiltonian (for normal people)
http://www.hyperblazer.net/research/fermion-dynamics-classical-hamiltonian-normal-people
Below is a "note" I wrote on Facebook to describe my research project on <a href="http://www.hyperblazer.net/research/fermion-dynamics-classical-hamiltonian">Fermion dynamics from a classical Hamiltonian</a>. Those of you with a solid background in molecular electronics (or even quantum mechanics generally) may recognize that I oversimplified a few points. But the purpose of this was more to explain why I'd been excited by this work than to teach people subtleties of the field of molecular electronics.
<hr />
<p><a href="http://www.hyperblazer.net/research/fermion-dynamics-classical-hamiltonian-normal-people">read more</a></p>ResearchTue, 02 Aug 2011 07:10:37 -060029 at http://www.hyperblazer.netFermion Dynamics from a Classical Hamiltonian
http://www.hyperblazer.net/research/fermion-dynamics-classical-hamiltonian
<p>While he was on sabbatical in Berkeley, Prof. Eran Rabani approached Prof. Miller about the idea of developing a semiclassical approach to study molecular electronics. Together, we developed what we eventually called the Dynamics for Classically Mapped Fermions (DCMF) method, which generates classical model Hamiltonian that can describe the dynamics of fermionic systems. Fermion dynamics are particularly challenging for a classical model because of the Pauli exclusion principle and because of the anticommutivity of fermionic operators.</p><p><a href="http://www.hyperblazer.net/research/fermion-dynamics-classical-hamiltonian">read more</a></p>ResearchFri, 25 Feb 2011 06:48:58 -070028 at http://www.hyperblazer.netTime Dependent Sampling and Path Sampling for Semiclassical IVRs
http://www.hyperblazer.net/research/time-dependent-sampling-and-path-sampling-semiclassical-ivrs
<p>In an effort to reduce the number of trajectories required for semiclassical calculations, I tried including information about the time-evolved distribution in the Monte Carlo sampling for the double Herman-Kluk (DHK) semiclassical initial value representation (IVR). Historically, we have sampled using only the distribution at time zero. However, many trajectories initiated from those initial conditions end up unimportant at later times. Our idea was to reduce the contributing trajectories to those which are also important at the later time of interest.<p><a href="http://www.hyperblazer.net/research/time-dependent-sampling-and-path-sampling-semiclassical-ivrs">read more</a></p>ResearchFri, 25 Feb 2011 06:41:28 -070027 at http://www.hyperblazer.netPrecision Finite Difference Monodromy Matrix
http://www.hyperblazer.net/research/precision-finite-difference-monodromy-matrix
<p>While at the University of California, Berkeley, I developed a new method for calculating the monodromy matrix. The monodromy (or stability) matrix is a quantity of central importance in many semiclassical theories; it is required to calculate the semiclassical prefactor, which helps capture many quantum effects in semiclassical calculations. Calculating it is one of the most computationally difficult parts of many semiclassical calculations.</p>
<p><a href="http://www.hyperblazer.net/research/precision-finite-difference-monodromy-matrix">read more</a></p>ResearchMon, 22 Nov 2010 19:09:23 -070025 at http://www.hyperblazer.netSemiclassical Dynamics of Constrained Systems
http://www.hyperblazer.net/research/semiclassical-dynamics-constrained-systems
<p>Under the direction of <a href="http://chem.berkeley.edu/people/faculty/miller/miller.html">William H. Miller</a> at <a href="http://www.berkeley.edu">The University of California, Berkeley</a>, I worked on applying the semiclassical initial value representation [1] to systems with arbitrary holonomic constraints.</p>
<p>The semiclassical initial value representation (SC-IVR) was originally developed by W.H. Miller in the early 1970s. As computers have improved, it has re-emerged as a practical method to include approximate quantum effects in a wide range of dynamical molecular properties. P.-N. Roy has recently explored the idea of adding constraints to the SC-IVR [2], and I've been working on possible improvements to the framework he developed.</p>
<p><a href="http://www.hyperblazer.net/research/semiclassical-dynamics-constrained-systems">read more</a></p>ResearchMon, 21 Jan 2008 09:26:22 -070010 at http://www.hyperblazer.netA Method for Solving Poisson Problems
http://www.hyperblazer.net/research/method-solving-poisson-problems
<p>Under the direction of Dr. Cristian Predescu (at the time a post-doctoral scholar at the University of California, Berkeley) I used a new grid-based integration scheme to solve model electrostatic problems. We found that the method scaled very well for the interior space once accurate boundary conditions had been established.</p>
<p>The results of this project were presented at the Mini Statistical Mechanics Meeting held in Berkeley in January 2007. <a href="http://www.hyperblazer.net/research/grid_poster.pdf">[Poster: 504K]</a></p>
ResearchMon, 21 Jan 2008 09:20:00 -070026 at http://www.hyperblazer.netModeling the potential energy surface of H2-benzene
http://www.hyperblazer.net/research/modeling-potential-energy-surface-h2-benzene
<p> Under the direction of <a href="http://chem.iupui.edu/Faculty/Dykstra/">Prof. Clifford E. Dykstra</a> of <a href="http://www.iupui.edu/">Indiana University-Purdue University Indianapolis</a>, I used the Molecular Mechanics for Clusters [1] scheme to develop an approximate version of the H<sub>2</sub>-benzene <i>ab initio</i> potential energy surface. Using previously developed parameters for the H<sub>2</sub>-H<sub>2</sub> interaction, [2] I was able to show that our model represented clusters of H<sub>2</sub> around a benzene with good accuracy.</p>
<p><a href="http://www.hyperblazer.net/research/modeling-potential-energy-surface-h2-benzene">read more</a></p>ResearchMon, 21 Jan 2008 09:16:24 -07009 at http://www.hyperblazer.net