Biomedical subjects

T Aspelmeier

Publications and source records attributed to T Aspelmeier.

8 recordsLinked to original sources

PubMed2004

Complexity of Ising spin glasses.

We compute the complexity [logarithm of the number of Thouless-Anderson-Palmer (TAP) states] associated with minima and index-one saddle points of the TAP free energy. Higher-index saddles have smaller complexities. The two leading complexities are equal, consistent with the Morse theorem on the total number of turning points, and have the value given by Bray and Moore [J. Phys. C, ()]]. In the thermodynamic limit, TAP states of all free energies become marginally stable.

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PubMed2004

Generalized Bose-Einstein phase transition in large-m component spin glasses.

It is proposed to understand finite dimensional spin glasses using a 1/m expansion, where m is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which the expansion is made, the infinite-m limit, has been studied in the mean-field limit in detail and has a very unusual phase transition, rather similar to a Bose-Einstein phase transition but with N(2/5) macroscopically occupied low-lying states.

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PubMed2003

Free energy fluctuations in Ising spin glasses.

The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number n. It is shown that the Parisi symmetry breaking scheme does not give the correct answers for these higher order terms. A modified symmetry breaking scheme with the same stability is shown to resolve the problem.

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PubMed2003

Interface energies in ising spin glasses.

The replica method has been used to calculate the interface free energy associated with the change from periodic to antiperiodic boundary conditions in finite-dimensional spin glasses. At mean-field level the interface free energy vanishes, but after allowing for fluctuation effects, a nonzero interface free energy is obtained which is significantly different from numerical expectations.

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PubMed2002

Why temperature chaos in spin glasses is hard to observe.

The overlap length of a three-dimensional Ising spin glass on a cubic lattice with Gaussian interactions has been estimated numerically by transfer matrix methods and within a Migdal-Kadanoff renormalization group scheme. We find that the overlap length is large, explaining why it has been difficult to observe spin glass chaos in numerical simulations and experiment.

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PubMed2001

Stress relaxation of near-critical gels.

The time-dependent stress relaxation for a Rouse model of a cross-linked polymer melt is completely determined by the spectrum of eigenvalues of the connectivity matrix. The latter has been computed analytically for a mean-field distribution of cross-links. It shows a Lifshitz tail for small eigenvalues and all concentrations below the percolation threshold, giving rise to a stretched exponential decay of the stress relaxation function in the sol phase. At the critical point the density of states is finite for small eigenvalues, resulting in a logarithmic divergence of the viscosity and an algebraic decay of the stress relaxation function. Numerical diagonalization of the connectivity matrix supports the analytical findings and has furthermore been applied to cluster statistics corresponding to random bond percolation in two and three dimensions.

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PubMed2001

Microscopic kinetics and time-dependent structure factors.

The time evolution of structure factors (SF) in the disordering process of an initially phase-separated lattice depends crucially on the microscopic disordering mechanism, such as Kawasaki dynamics (KD) or vacancy-mediated disordering (VMD). Monte Carlo simulations show unexpected "dips" in the SFs. A phenomenological model is introduced to explain the dips in the odd SFs, and an analytical solution of KD is derived, in excellent agreement with simulations. The presence (absence) of dips in the even SFs for VMD (KD) marks a significant but not yet understood difference of the two dynamics.

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PubMed1999

Granular cooling of hard needles.

We have developed a kinetic theory of hard needles undergoing binary collisions with loss of energy due to normal and tangential restitution. In addition, we have simulated many particle systems of granular hard needles. The theory, based on the assumption of a homogeneous cooling state, predicts that granular cooling of the needles proceeds in two stages: An exponential decay of the initial configuration to a state where translational and rotational energies take on a time independent ratio (different from unity), followed by an algebraic decay of the total kinetic energy of approximately t(-2). The simulations support the theory very well for low and moderate densities. For higher densities, we have observed the onset of the formation of clusters and shear bands.

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