Modelling Molecular Motors as Folding-Unfolding Cycles

We propose a model for motor proteins based on a hierarchical Hamiltonian that we have previously introduced to describe protein folding. The proposed motor model has high efficiency and is consistent with a linear load-velocity response. The main improvement with respect to previous models is that this description suggests a connection between folding and function of allosteric proteins.Comment: 5 pages RevTeX, 2 Postscript figures, replaced due to LaTeX proble

Coherent Control for a Two-level System Coupled to Phonons

The interband polarizations induced by two phase-locked pulses in a semiconductor show strong interference effects depending on the time tau_1 separating the pulses. The four-wave mixing signal diffracted from a third pulse delayed by tau is coherently controlled by tuning tau_1. The four-wave mixing response is evaluated exactly for a two-level system coupled to a single LO phonon. In the weak coupling regime it shows oscillations with the phonon frequency which turn into sharp peaks at multiples of the phonon period for a larger coupling strength. Destructive interferences between the two phase-locked pulses produce a splitting of the phonon peaks into a doublet. For fixed tau but varying tau_1 the signal shows rapid oscillations at the interband-transition frequency, whose amplitude exhibits bursts at multiples of the phonon period.Comment: 4 pages, 4 figures, RevTex, content change

Gel-Electrophoresis and Diffusion of Ring-Shaped DNA

A model for the motion of ring-shaped DNA in a gel is introduced and studied by numerical simulations and a mean-field approximation. The ring motion is mediated by finger-shaped loops (hernias) that move in an amoeba-like fashion around the gel obstructions. This constitutes an extension of previous reptation tube treatments. It is shown that tension is essential for describing the dynamics in the presence of hernias. It is included in the model as long range interactions over stretched DNA regions. The mobility of ring-shaped DNA is found to saturate much as in the well-studied case of linear DNA. Experiments in polymer gels, however, show that the mobility drops exponentially with the DNA ring size. This is commonly attributed to dangling-ends in the gel that can impale the ring. The predictions of the present model are expected to apply to artificial 2D obstacle arrays (W.D. Volkmuth, R.H. Austin, Nature 358,600 (1992)) which have no dangling-ends. In the zero-field case an exact solution of the model steady-state is obtained, and quantities such as the average ring size are calculated. An approximate treatment of the ring dynamics is given, and the diffusion coefficient is derived. The model is also discussed in the context of spontaneous symmetry breaking in one dimension.Comment: 8 figures, LaTeX, Phys. Rev. E - in pres

Equidistribution of Heegner Points and Ternary Quadratic Forms

We prove new equidistribution results for Galois orbits of Heegner points with respect to reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize one of the equidistribution theorems established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system

Exploring AI Futures Through Role Play

We present an innovative methodology for studying and teaching the impacts of AI through a role play game. The game serves two primary purposes: 1) training AI developers and AI policy professionals to reflect on and prepare for future social and ethical challenges related to AI and 2) exploring possible futures involving AI technology development, deployment, social impacts, and governance. While the game currently focuses on the inter relations between short --, mid and long term impacts of AI, it has potential to be adapted for a broad range of scenarios, exploring in greater depths issues of AI policy research and affording training within organizations. The game presented here has undergone two years of development and has been tested through over 30 events involving between 3 and 70 participants. The game is under active development, but preliminary findings suggest that role play is a promising methodology for both exploring AI futures and training individuals and organizations in thinking about, and reflecting on, the impacts of AI and strategic mistakes that can be avoided today.Comment: Accepted to AIE

The subconvexity problem for \GL_{2}

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of \GL_{1} and \GL_{2} automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino--Ikeda.Comment: Almost final version to appear in Publ. Math IHES. References updated

Effects of Parton Intrinsic Transverse Momentum on Photon Production in Hard-Scattering Processes

We calculate the photon production cross section arising from the hard scattering of partons in nucleon-nucleon collisions by taking into account the intrinsic parton transverse momentum distribution and the next-to-leading-order contributions. As first pointed out by Owens, the inclusion of the intrinsic transverse momentum distribution of partons leads to an enhancement of photon production cross section in the region of photon transverse momenta of a few GeV/c for nucleon-nucleon collisions at a center-of-mass energy of a few tens of GeV. The enhancement increases as $\sqrt{s}$ decreases. Such an enhancement is an important consideration in the region of photon momenta under investigation in high-energy heavy-ion collisions.Comment: 10 pages, 9 figures, in LaTex, revised to include ananlytic evaluation of the hard-scattering integra

Multiple timescales in a model for DNA denaturation dynamics

The denaturation dynamics of a long double-stranded DNA is studied by means of a model of the Poland-Scheraga type. We note that the linking of the two strands is a locally conserved quantity, hence we introduce local updates that respect this symmetry. Linking dissipation via untwist is allowed only at the two ends of the double strand. The result is a slow denaturation characterized by two time scales that depend on the chain length $L$. In a regime up to a first characteristic time $\tau_1\sim L^{2.15}$ the chain embodies an increasing number of small bubbles. Then, in a second regime, bubbles coalesce and form entropic barriers that effectively trap residual double-stranded segments within the chain, slowing down the relaxation to fully molten configurations, which takes place at $\tau_2\sim L^3$. This scenario is different from the picture in which the helical constraints are neglected.Comment: 9 pages, 5 figure

Quantum heat transfer through an atomic wire

We studied the phononic heat transfer through an atomic dielectric wire with both infinite and finite lengths by using a model Hamiltonian approach. At low temperature under ballistic transport, the thermal conductance contributed by each phonon branch of a uniform and harmonic chain cannot exceed the well-known value which depends linearly on temperature but is material independent. We predict that this ballistic thermal conductance will exhibit stepwise behavior as a function of temperature. By performing numerical calculations on a more realistic system, where a small atomic chain is placed between two reservoirs, we also found resonance modes, which should also lead to the stepwise behavior in the thermal conductance.Comment: 14 pages, 2 separate figure

Collective dynamics in crystalline polymorphs of ZnCl2_{2}: potential modelling and inelastic neutron scattering study

We report a phonon density of states measurement of $\alpha$-ZnCl$_{2}$ using the coherent inelastic neutron scattering technique and a lattice dynamical calculation in four crystalline phases of ZnCl$_{2}$ using a transferable interatomic potential. The model calculations agree reasonably well with the available experimental data on the structures, specific heat, Raman frequencies and their pressure variation in various crystalline phases. The calculated results have been able to provide a fair description of the vibrational as well as the thermodynamic properties of ZnCl$_{2}$ in all its four phases.Comment: Accepted in J. Phys.: Condens. Matte