J. Franklin

MinActionPath: maximum likelihood trajectory for large-scale structural transitions in a coarse-grained locally harmonic energy landscape.

The non-linear problem of simulating the structural transition between two known forms of a macromolecule still remains a challenge in structural biology. The problem is usually addressed in an approximate way using ‘morphing’ techniques, which are linear interpolations of either the Cartesian or the internal coordinates between the initial and end states, followed by energy minimization. Here we describe a web tool that implements a new method to calculate the most probable trajectory that is exact for harmonic potentials; as an illustration of the method, the classical Calpha-based Elastic Network Model (ENM) is used both for the initial and the final states but other variants of the ENM are also possible. The Langevin equation under this potential is solved analytically using the Onsager and Machlup action minimization formalism on each side of the transition, thus replacing the original non-linear problem by a pair of linear differential equations joined by a non-linear boundary matching condition. The crossover between the two multidimensional energy curves around each state is found numerically using an iterative approach, producing the most probable trajectory and fully characterizing the transition state and its energy. Jobs calculating such trajectories can be submitted on-line at: http://lorentz.dynstr.pasteur.fr/joel/index.php.

Approximate Born–Infeld effects on the relativistic hydrogen spectrum

Abstract The Born–Infeld form of the hydrogen atom has a spectrum that can be used to determine the physical viability of the theory, and place an experimentally relevant bound on the single parameter found in it. We compute this spectrum using the relativistic Dirac equation, and a form of the Born–Infeld potential that approximates the self-field corrections of the electron. Using these together, we can establish that if the Born–Infeld nonlinear electrodynamics is to be physically relevant, it must contain a fundamental constant that is well below the original value proposed by Born. This work extends the original Schrodinger spectrum from Carley and Kiessling (2006) [1] for the self-field correction, and shows that using the Dirac equation introduces minor corrections – but also gives access to a range for the fundamental constant that is below that attainable from non-relativistic considerations.

Circular symmetry in topologically massive gravity

We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null.

Linearized Kerr and spinning massive bodies: An electrodynamics analogy

We discuss the correspondence between spinning, charged spherical sources in electrodynamics and spinning, massive spherical sources in linearized general relativity and show that the form of the potentials and equations of motion are similar in the two cases in the slow motion limit. This similarity allows us to interpret the Kerr metric in analogy with a spinning sphere in electrodynamics and aids in understanding linearized general relativity, where the “forces” are effective and come from the intrinsic curvature of space-time.

The fields of a charged particle in hyperbolic motion

A particle in hyperbolic motion produces electric fields that appear to terminate in mid-air, violating Gausss law. The resolution to this paradox has been known for sixty years but exactly why the naive approach fails is not so clear.

Is BTZ a separate superselection sector of CTMG

We exhibit exact solutions of (positive) matter coupled to original “wrong G-sign” cosmological TMG. They all evolve to conical singularity, rather than to black hole – here negative mass – BTZ. This provides evidence that the latter constitute a separate “superselection” sector, one that unlike in GR, is not reachable by physical sources.

Computational Methods for Physics

There is an increasing need for undergraduate students in physics to have a core set of computational tools. Most problems in physics benefit from numerical methods, and many of them resist analytical solution altogether. This textbook presents numerical techniques for solving familiar physical problems where a complete solution is inaccessible using traditional mathematical methods. The numerical techniques for solving the problems are clearly laid out, with a focus on the logic and applicability of the method. The same problems are revisited multiple times using different numerical techniques, so readers can easily compare the methods. The book features over 250 end-of-chapter exercises. A website hosted by the author features a complete set of programs used to generate the examples and figures, which can be used as a starting point for further investigation. A link to this can be found at www.cambridge.org/9781107034303.

Time (in)dependence in general relativity

We clarify the conditions for Birkhoffs theorem, that is, time independence in general relativity. We work primarily at the linearized level where guidance from electrodynamics is particularly useful. As a bonus, we also review how the equivalence principle results from general relativity. The basic time-independent solutions due to Schwarzschild and Kerr provide concrete illustrations of the theorem. Only familiarity with Maxwells equations and tensor analysis is required.

The Schrödinger–Newton system with self-field coupling

We study the Schrodinger–Newton (SN) system of equations with the addition of gravitational field energy sourcing—such additional nonlinearity is to be expected from a theory of gravity (like general relativity (GR)), and its appearance in this simplified scalar setting (one of Einsteins precursors to GR) leads to significant changes in the spectrum of the self-gravitating theory. Using an iterative technique, we compare the mass dependence of the ground state energies of both SN and the new, self-sourced system and find that they are dramatically different. The Bohr method approach from old quantization provides a qualitative description of the difference, which comes from the additional nonlinearity introduced in the self-sourced case. In addition to comparison of ground state energies, we calculate the transition energy between the ground state and first excited state to compare emission frequencies between SN and the self-coupled scalar case.

Self-consistent, self-coupled scalar gravity

A scalar theory of gravity, extending Newtonian gravity to include field energy as its source, is developed. The physical implications of the theory are probed through its spherically symmetric (source) solutions. The aim is to demonstrate rational physical model building, together with physical and experimental checks of correctness. The theory discussed here was originally considered by Einstein prior to his introduction of general relativity.