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Release currents of IP₃ receptor channel clusters and concentration profiles (2004)
Journal Article
Thul, R., & Falcke, M. (2004). Release currents of IP₃ receptor channel clusters and concentration profiles. Biophysical Journal, 86(5),

We simulate currents and concentration profiles generated by Ca2+ release from the endoplasmic reticulum (ER)
to the cytosol through IP3 receptor channel clusters. Clusters are described as conducting pores in the lumenal membrane with a diameter f... Read More about Release currents of IP₃ receptor channel clusters and concentration profiles.

Stability of membrane bound reactions (2004)
Journal Article
Thul, R., & Falcke, M. (2004). Stability of membrane bound reactions. Physical Review Letters, 93(18), https://doi.org/10.1103/+PhysRevLet+t.93.188103

We present a novel approach to the dynamics of reactions of diffusing chemical species with species fixed in space e.g. by binding to a membrane. The non-diffusing reaction partners are clustered in areas with a diameter smaller than the diffusion length... Read More about Stability of membrane bound reactions.

Nonlinear breathing modes at a defect (2004)
Journal Article
Wattis, J. A. (2004). Nonlinear breathing modes at a defect. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 362,

Recent molecular dynamics (MD) simulations of Cubero et al (1999) of
a DNA duplex containing the 'rogue' base difluorotoluene (F) in place of a
thymine (T) base show that breathing events can occur on the nanosecond
timescale, whereas breathing ev... Read More about Nonlinear breathing modes at a defect.

Landau-Gutzwiller quasi-particles (2003)
Journal Article
Bünemann, J., Gebhard, F., & Thul, R. (2003). Landau-Gutzwiller quasi-particles. Physical Review B, 67, Article 075103. https://doi.org/10.1103/PhysRevB.67.075103

We define Landau quasiparticles within the Gutzwiller variational theory and derive their dispersion relation for general multiband Hubbard models in the limit of large spatial dimensions D. Thereby we reproduce our previous calculations which were ba... Read More about Landau-Gutzwiller quasi-particles.

Efficient Solution of Rational Conics (2002)
Journal Article
Cremona, J. E., & Rusin, D. (2003). Efficient Solution of Rational Conics. Mathematics of Computation, 72(243), 1417-1441. https://doi.org/10.1090/S0025-5718-02-01480-1

We present efficient algorithms for solving Legendre equations over Q (equivalently, for finding rational points on rational conics) and parametrizing all solutions. Unlike existing algorithms, no integer factorization is required, provided that the... Read More about Efficient Solution of Rational Conics.

Spectral synthesis and topologies on ideal spaces for Banach *-algebras (2002)
Journal Article
Feinstein, J., Kaniuth, E., & Somerset, D. (2002). Spectral synthesis and topologies on ideal spaces for Banach *-algebras. Journal of Functional Analysis, 196(1), https://doi.org/10.1006/jfan.2002.3964

This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a fini... Read More about Spectral synthesis and topologies on ideal spaces for Banach *-algebras.

Predicting arsenic solubility in contaminated soils using isotopic dilution techniques (2002)
Journal Article
Tye, A. M., Young, S. D., Crout, N. M., Zhang, H., Preston, S., Bailey, E. H., Davison, W., McGrath, S. P., Paton, G. I., & Kilham, K. (2002). Predicting arsenic solubility in contaminated soils using isotopic dilution techniques. Environmental Science and Technology, 36(5), 982-988. https://doi.org/10.1021/es0101633

An isotopic dilution assay was developed to measure radiolabile As concentration in a diverse range of soils (pH 3.30-7.62; % C = 1.00-6.55). Soils amended with 50 mg of As kg-1 (as Na2HAsO4·7H2O) were incubated for over 800 d in an aerated "microcos... Read More about Predicting arsenic solubility in contaminated soils using isotopic dilution techniques.

Integrability for Relativistic Spin Networks (2001)
Journal Article
Barrett, J. W., & Baez, J. C. (2001). Integrability for Relativistic Spin Networks. Classical and Quantum Gravity, 18(4683-4),

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lo... Read More about Integrability for Relativistic Spin Networks.

A Lorentzian Signature Model for Quantum General Relativity (2000)
Journal Article
Barrett, J. W., & Crane, L. (2000). A Lorentzian Signature Model for Quantum General Relativity

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra.
We propose a combinatorial model for the path integral given by an integral over suitable representations of... Read More about A Lorentzian Signature Model for Quantum General Relativity.

The asymptotics of an amplitude for the 4-simplex (1999)
Journal Article
Barrett, J. W., & Williams, R. M. (1999). The asymptotics of an amplitude for the 4-simplex. https://doi.org/10.4310/atmp.1999.v3.n2.a1

An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given. The amplitude depends on specified areas for each two-dimensional face in the 4-simplex. The asymptotic formula has... Read More about The asymptotics of an amplitude for the 4-simplex.

Hexagonal patterns in finite domains (1998)
Journal Article
Matthews, P. (1998). Hexagonal patterns in finite domains. Physica D: Nonlinear Phenomena, 116,

In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the possible patt... Read More about Hexagonal patterns in finite domains.

The classical evaluation of relativistic spin networks (1998)
Journal Article
Barrett, J. W. (1998). The classical evaluation of relativistic spin networks. https://doi.org/10.4310/atmp.1998.v2.n3.a7

The evaluation of a relativistic spin network for the classical case of the Lie group SU(2) is given by an integral formula over copies of SU(2). For the graph determined by a 4-simplex this gives the evaluation as an integral over a space of geometr... Read More about The classical evaluation of relativistic spin networks.

Floating s- and p-type Gaussian Orbitals (1975)
Journal Article
Brailsford, D. F., Hall, G. G., Hemming, N., & Martin, D. (1975). Floating s- and p-type Gaussian Orbitals. Chemical Physics Letters, 35(4), https://doi.org/10.1016/0009-2614%2875%2985638-7

The advantages of including a small number of p-type gaussian functions in a floating spherical gaussian orbital calculation are pointed out and illustrated by calculations on molecules which previously have proved to be troublesome. These include mo... Read More about Floating s- and p-type Gaussian Orbitals.

Approximate ab initio calculations and the method of molecular fragments (1975)
Presentation / Conference Contribution
Brailsford, D. F. Approximate ab initio calculations and the method of molecular fragments. Presented at Quantum Chemistry - The State of the Art

A two stage approach to performing ab initio calculations on medium and large sized molecules is described. The first step is to perform SCF calculations on small molecules or molecular fragments using the OPIT Program. This employs a small basis set... Read More about Approximate ab initio calculations and the method of molecular fragments.