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.

Fast parallel algorithms for short-range molecular dynamics

We consider holography for d-dimensional scale invariant but non-Lorentz invariant field theories, which do not admit the full Schrodinger symmetry group. We find new realizations of the corresponding (d+1)-dimensional gravity duals, engineered with a variety of matter Lagrangians, and their finite temperature generalizations. The thermodynamic properties of the finite temperature backgrounds are precisely those expected for anisotropic, scale invari- ant field theories. The brane and string theory realizations of such backgrounds are briefly discussed, along with their holographic interpretation in terms of marginal but non Lorentz invariant deformations of conformal field theories. We initiate discussion of holographic renormalization in these backgrounds, and note that such systematic renormalization is necessary to obtain the correct behavior of correlation functions.

Non-relativistic holography

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1397398

Cosmological Inflation and Large-Scale Structure

A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.

https://science.sciencemag.org/content/sci/325/5939/439.full.pdf

String Theory, Quantum Phase Transitions, and the Emergent Fermi Liquid

These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.

Holographic Duality with a View Toward Many-Body Physics

We study a new contraction of a d+1 dimensional relativistic conformal algebra where n+1 directions remain unchanged. For n = 0,1 the resultant algebras admit infinite dimensional extension containing one and two copies of Virasoro algebra, respectively. For 1$>n>1 the obtained algebra is finite dimensional containing an so(2,n+1) subalgebra. The gravity dual is provided by taking a Newton-Cartan like limit of the Einstein's equations of AdS space which singles out an AdSn+2 spacetime. The infinite dimensional extension of n = 0,1 cases may be understood from the fact that the dual gravities contain AdS2 and AdS3 factor, respectively. We also explore how the AdS/CFT correspondence works for this case where we see that the main role is playing by AdSn+2 base geometry.

On AdS/CFT of Galilean Conformal Field Theories

https://mmzaeri.mech.iut.ac.ir/sites/mech.iut.ac.ir/files/upload_publications/mechanical_modelling_of_carbon_nanomaterials_from_nanotubes_to_buckypaper.pdf

Mechanical modelling of carbon nanomaterials from nanotubes to buckypaper

We study different features of 3D non-relativistic CFT using gravity description. As the corresponding gravity solution can be embedded into the type IIB string theory, we study semi-classical closed/open strings in this background. In particular we consider folded rotating and circular pulsating closed strings where we find the anomalous dimension of the dual operators as a function of their quantum numbers. We also consider moving open strings in this background which can be used to compute the drag force. In particular we find that for slowly moving particles, the energy is lost exponentially and the characteristic time is given in terms of the temperature, while for fast moving particles the energy loss goes as inverse of the time and the characteristic time is independent of the temperature.

https://iopscience.iop.org/article/10.1088/1126-6708/2009/03/053/pdf

Non-relativistic CFT and Semi-classical Strings

We extend the nonrelativistic AdS/CFT correspondence to the fermionic fields. In particular, we study the two point function of a fermionic operator in nonrelativistic CFTs by making use of a massive fermion propagating in geometries with Schr\"odinger group isometry. Although the boundary of the geometries with Schr\"odinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in nonrelativistic CFTs, though a nontrivial regularization may be needed.

/pdf/fermions-in-nonrelativistic-ads-cft-correspondence-4b32zt95mh.pdf

Fermions in nonrelativistic AdS/CFT correspondence

Epoxy is among the most important polymers, which is extensively employed in various technologies and applications. Nevertheless, epoxy polymers present low thermal conductivities and thus the enhancement of their thermal conductivity is an important research topic. Carbon nanotubes (CNTs) owing to their excellent thermal conductivities have been widely considered for the enhancement of the thermal conduction of epoxy polymers. In this work, we developed a combined molecular dynamics finite element multiscale modelling to investigate the heat transfer along CNT/epoxy nanocomposites. To this aim, the heat transfer between the CNT and epoxy atoms at the nanoscale was explored using the atomistic classical molecular dynamics simulations. In this case, we particularly evaluated the interfacial thermal conductance between the polymer and fillers. We finally constructed the continuum models of polymer nanocomposites representative volume elements using the finite element method in order to evaluate the effective thermal conductivity. The developed multiscale modelling enabled us to systematically analyze the effects of CNT fillers geometry (aspect ratio), diameter and volume fraction on the effective thermal conductivity of nanocomposites. Our results suggest that the interfacial thermal conductance between the CNT additives and epoxy polymer dominate the heat transfer mechanism at the nanoscale. The obtained findings in this study provide good vision regarding the enhancement of thermal conductivity of polymeric materials using highly conductive nanofillers.

Ali Vahedi

Papers

On AdS/CFT of Galilean Conformal Field Theories

Mechanical modelling of carbon nanomaterials from nanotubes to buckypaper

Non-relativistic CFT and Semi-classical Strings

Fermions in nonrelativistic AdS/CFT correspondence

Multiscale modeling of thermal conductivity of carbon nanotube epoxy nanocomposites