Jordanian Solutions of Simplex Equations

We construct for all $N$ a solution of the Frenkel--Moore $N$--simplex equation which generalizes the $R$--matrix for the Jordanian quantum group.Comment: 6 page

The Self-Force of a Charged Particle in Classical Electrodynamics with a Cut-off

We discuss, in the context of classical electrodynamics with a Lorentz invariant cut-off at short distances, the self-force acting on a point charged particle. It follows that the electromagnetic mass of the point charge occurs in the equation of motion in a form consistent with special relativity. We find that the exact equation of motion does not exhibit runaway solutions or non-causal behavior, when the cut-off is larger than half of the classical radius of the electron.Comment: 17 pages, 1 figur

The Structure of Langevin's Memory Kernel From Lagrangian Dynamics

We obtain the memory kernel of the generalized Langevin equation, describing a particle interacting with longitudinal phonons in a liquid. The kernel is obtained analytically at T=0 Kelvin and numerically at T>0 Kelvin. We find that it shows some non-trivial structural features like negative correlations for some range of time separations. The system is shown to have three characteristic time scales, that control the shape of the kernel, and the transition between quadratic and linear behavior of the mean squared distance (MSD). Although the derivation of the structure in the memory kernel is obtained within a specific dynamical model, the phenomenon is shown to be quite generic.Comment: 8 pages, 5 figures, latex, include europhys.sty and euromacr.te

Howe Pairs in the Theory of Vertex Algebras

For any vertex algebra V and any subalgebra A of V, there is a new subalgebra of V known as the commutant of A in V. This construction was introduced by Frenkel-Zhu, and is a generalization of an earlier construction due to Kac-Peterson and Goddard-Kent-Olive known as the coset construction. In this paper, we interpret the commutant as a vertex algebra notion of invariant theory. We present an approach to describing commutant algebras in an appropriate category of vertex algebras by reducing the problem to a question in commutative algebra. We give an interesting example of a Howe pair (ie, a pair of mutual commutants) in the vertex algebra setting.Comment: A few typos corrected, final versio

Understanding the nucleation mechanisms of Carbon Nanotubes in catalytic Chemical Vapor Deposition

The nucleation of carbon caps on small nickel clusters is studied using a tight binding model coupled to grand canonical Monte Carlo simulations. It takes place in a well defined carbon chemical potential range, when a critical concentration of surface carbon atoms is reached. The solubility of carbon in the outermost Ni layers, that depends on the initial, crystalline or disordered, state of the catalyst and on the thermodynamic conditions, is therefore a key quantity to control the nucleation

Causes of Appreciation and Volatility of the Dollar with Comment by Jacob Frenkel

In 1981 real interest rates in the United States increased spectacularly, and the dollar appreciated in real terms by about 20 percent. Since the end of 1981, long-term real interest rates have remained in the range of 5-10 percent, with nominal long rates above short rates. The dollar appreciated further, but more gradually, until early 1985. This paper argues that these movements in real interest rates and the real exchange rate are due to the shift in the high-employment deficit by some $200 billion that was announced in the 1981 budget program. This requires an increase in real interest rates and a real appreciation to generate the sum of excess domestic saving and foreign borrowing to finance it. The argument is a straightforward extension of the idea of "crowding out" at full employment to an open economy.The current situation is not sustainable, however. Eventually international investors will begin to resist further absorption of dollars into their portfolios, so U.S. interest rates will have to rise further, as the markets seem to expect, and the dollar will have to depreciate. This will continue until the current account is back in approximate balance, and the entire load of deficit financing is shifted to excess U.S. saving. In his comments on Branson's paper, Jacob A. Frenkel discusses additional factors that have contributed to the evolution of the dollar since 1980. He concludes that in addition to U.S. fiscal policies, monetary policy in the United States and the fiscal position of the U.K., West Germany and Japan have also contributed to the dollar's strength.

Non Abelian Sugawara Construction and the q-deformed N=2 Superconformal Algebra

The construction of a q-deformed N=2 superconformal algebra is proposed in terms of level 1 currents of ${\cal{U}}_{q} ({\widehat{su}}(2))$ quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to ${\cal{U}}_{q} ({\widehat{su}}(N+1))$ is also proposed.Comment: AMSLATEX, 21page

Estimating statistical distributions using an integral identity

We present an identity for an unbiased estimate of a general statistical distribution. The identity computes the distribution density from dividing a histogram sum over a local window by a correction factor from a mean-force integral, and the mean force can be evaluated as a configuration average. We show that the optimal window size is roughly the inverse of the local mean-force fluctuation. The new identity offers a more robust and precise estimate than a previous one by Adib and Jarzynski [J. Chem. Phys. 122, 014114, (2005)]. It also allows a straightforward generalization to an arbitrary ensemble and a joint distribution of multiple variables. Particularly we derive a mean-force enhanced version of the weighted histogram analysis method (WHAM). The method can be used to improve distributions computed from molecular simulations. We illustrate the use in computing a potential energy distribution, a volume distribution in a constant-pressure ensemble, a radial distribution function and a joint distribution of amino acid backbone dihedral angles.Comment: 45 pages, 7 figures, simplified derivation, a more general mean-force formula, add discussions to the window size, add extensions to WHAM, and 2d distribution

A general theory of DNA-mediated and other valence-limited interactions

We present a general theory for predicting the interaction potentials between DNA-coated colloids, and more broadly, any particles that interact via valence-limited ligand-receptor binding. Our theory correctly incorporates the configurational and combinatorial entropic factors that play a key role in valence-limited interactions. By rigorously enforcing self-consistency, it achieves near-quantitative accuracy with respect to detailed Monte Carlo calculations. With suitable approximations and in particular geometries, our theory reduces to previous successful treatments, which are now united in a common and extensible framework. We expect our tools to be useful to other researchers investigating ligand-mediated interactions. A complete and well-documented Python implementation is freely available at http://github.com/patvarilly/DNACC .Comment: 18 pages, 10 figure