A Finite-Size Scaling Study of a Model of Globular Proteins

Grand canonical Monte Carlo simulations are used to explore the metastable fluid-fluid coexistence curve of the modified Lennard-Jones model of globular proteins of ten Wolde and Frenkel (Science, v277, 1975 (1997)). Using both mixed-field finite-size scaling and histogram reweighting methods, the joint distribution of density and energy fluctuations is analyzed at coexistence to accurately determine the critical-point parameters. The subcritical coexistence region is explored using the recently developed hyper-parallel tempering Monte Carlo simulation method along with histogram reweighting to obtain the density distributions. The phase diagram for the metastable fluid-fluid coexistence curve is calculated in close proximity to the critical point, a region previously unattained by simulation.Comment: 17 pages, 10 figures, 2 Table

Time-dependent perturbation theory for vibrational energy relaxation and dephasing in peptides and proteins

Without invoking the Markov approximation, we derive formulas for vibrational energy relaxation (VER) and dephasing for an anharmonic system oscillator using a time-dependent perturbation theory. The system-bath Hamiltonian contains more than the third order coupling terms since we take a normal mode picture as a zeroth order approximation. When we invoke the Markov approximation, our theory reduces to the Maradudin-Fein formula which is used to describe VER properties of glass and proteins. When the system anharmonicity and the renormalization effect due to the environment vanishes, our formulas reduce to those derived by Mikami and Okazaki invoking the path-integral influence functional method [J. Chem. Phys. 121 (2004) 10052]. We apply our formulas to VER of the amide I mode of a small amino-acide like molecule, N-methylacetamide, in heavy water.Comment: 16 pages, 5 figures, 5 tables, submitted to J. Chem. Phy

Instantaneous Pair Theory for High-Frequency Vibrational Energy Relaxation in Fluids

Notwithstanding the long and distinguished history of studies of vibrational energy relaxation, exactly how it is that high frequency vibrations manage to relax in a liquid remains somewhat of a mystery. Both experimental and theoretical approaches seem to say that there is a natural frequency range associated with intermolecular motions in liquids, typically spanning no more than a few hundred cm^{-1}. Landau-Teller-like theories explain how a solvent can absorb any vibrational energy within this "band", but how is it that molecules can rid themselves of superfluous vibrational energies significantly in excess of these values? We develop a theory for such processes based on the idea that the crucial liquid motions are those that most rapidly modulate the force on the vibrating coordinate -- and that by far the most important of these motions are those involving what we have called the mutual nearest neighbors of the vibrating solute. Specifically, we suggest that whenever there is a single solvent molecule sufficiently close to the solute that the solvent and solute are each other's nearest neighbors, then the instantaneous scattering dynamics of the solute-solvent pair alone suffices to explain the high frequency relaxation. The many-body features of the liquid only appear in the guise of a purely equilibrium problem, that of finding the likelihood of particularly effective solvent arrangements around the solute. These results are tested numerically on model diatomic solutes dissolved in atomic fluids (including the experimentally and theoretically interesting case of I_2 in Xe). The instantaneous pair theory leads to results in quantitative agreement with those obtained from far more laborious exact molecular dynamics simulations.Comment: 55 pages, 6 figures Scheduled to appear in J. Chem. Phys., Jan, 199

Afterlife: the post-research affect and effect of software

Software plays an important role in contemporary research. Aside from its use for administering traditional instruments like surveys and in data analysis, the widespread use of mobile and web apps for social, medical and lifestyle engagement has led to software becoming a research intervention in its own right. For example, it is not unusual to find apps being studied for their utility as interventions in health and social life. Since the software may persist in use beyond the life of an investigation, this raises questions as to the extent of ethical duties for researchers involved in its production and/or study towards the participants involved. Key factors identified include the extent of affect created by the software, the effect it has on a participant’s life, the length of investigation, cost of maintenance and participant agency. In this article we discuss the issues raised in such situations, considering them in the context of post-research duties of care and suggesting strategies to balance the burden on researchers with the need for ongoing participant support

A counterexample to well-posedness of entropy solutions to the compressible Euler system

We deal with entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the space-periodic case. In more than one space dimension, the methods developed by De Lellis-Sz\'ekelyhidi enable us to show failure of uniqueness on a finite time-interval for entropy solutions starting from any continuously differentiable initial density and suitably constructed bounded initial linear momenta.Comment: 29 page

Discrete Klein-Gordon models with static kinks free of the Peierls-Nabarro potential

For the nonlinear Klein-Gordon type models, we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice. These discrete models are therefore free of the {\it static} Peierls-Nabarro potential. Previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method. A relevant physical consequence of our findings is the existence of a wide class of discrete Klein-Gordon models where slow kinks {\it practically} do not experience the action of the Peierls-Nabarro potential. Such kinks are not trapped by the lattice and they can be accelerated by even weak external fields.Comment: 6 pages, 2 figure

Normal form for travelling kinks in discrete Klein-Gordon lattices

We study travelling kinks in the spatial discretizations of the nonlinear Klein--Gordon equation, which include the discrete $\phi^4$ lattice and the discrete sine--Gordon lattice. The differential advance-delay equation for travelling kinks is reduced to the normal form, a scalar fourth-order differential equation, near the quadruple zero eigenvalue. We show numerically non-existence of monotonic kinks (heteroclinic orbits between adjacent equilibrium points) in the fourth-order equation. Making generic assumptions on the reduced fourth-order equation, we prove the persistence of bounded solutions (heteroclinic connections between periodic solutions near adjacent equilibrium points) in the full differential advanced-delay equation with the technique of center manifold reduction. Existence and persistence of multiple kinks in the discrete sine--Gordon equation are discussed in connection to recent numerical results of \cite{ACR03} and results of our normal form analysis

Quantum trajectories for the realistic measurement of a solid-state charge qubit

We present a new model for the continuous measurement of a coupled quantum dot charge qubit. We model the effects of a realistic measurement, namely adding noise to, and filtering, the current through the detector. This is achieved by embedding the detector in an equivalent circuit for measurement. Our aim is to describe the evolution of the qubit state conditioned on the macroscopic output of the external circuit. We achieve this by generalizing a recently developed quantum trajectory theory for realistic photodetectors [P. Warszawski, H. M. Wiseman and H. Mabuchi, Phys. Rev. A_65_ 023802 (2002)] to treat solid-state detectors. This yields stochastic equations whose (numerical) solutions are the ``realistic quantum trajectories'' of the conditioned qubit state. We derive our general theory in the context of a low transparency quantum point contact. Areas of application for our theory and its relation to previous work are discussed.Comment: 7 pages, 2 figures. Shorter, significantly modified, updated versio

Strong Attraction between Charged Spheres due to Metastable Ionized States

We report a mechanism which can lead to long range attractions between like-charged spherical macroions, stemming from the existence of metastable ionized states. We show that the ground state of a single highly charged colloid plus a few excess counterions is overcharged. For the case of two highly charged macroions in their neutralizing divalent counterion solution we demonstrate that, in the regime of strong Coulomb coupling, the counterion clouds are very likely to be unevenly distributed, leading to one overcharged and one undercharged macroion. This long-living metastable configuration in turn leads to a long range Coulomb attraction.Comment: REVTEX-published versio

Scanning Quantum Decoherence Microscopy

The use of qubits as sensitive magnetometers has been studied theoretically and recent demonstrated experimentally. In this paper we propose a generalisation of this concept, where a scanning two-state quantum system is used to probe the subtle effects of decoherence (as well as its surrounding electromagnetic environment). Mapping both the Hamiltonian and decoherence properties of a qubit simultaneously, provides a unique image of the magnetic (or electric) field properties at the nanoscale. The resulting images are sensitive to the temporal as well as spatial variation in the fields created by the sample. As an example we theoretically study two applications of this technology; one from condensed matter physics, the other biophysics. The individual components required to realise the simplest version of this device (characterisation and measurement of qubits, nanoscale positioning) have already been demonstrated experimentally.Comment: 11 pages, 5 low quality (but arXiv friendly) image