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Compressibility and the Algorithmic Theory of Laws
2019
Principia: An International Journal of Epistemology
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This paper evaluates these sources and argues that none provides a convincing case to reject the algorithmic theory of laws. ...
The algorithmic theory of laws claims that the laws of nature are the algorithms in the best possible compression of all empirical data. ...
Very few algorithms can reproduce data without the need of additional, unstructured singular data to "work with". ...
doi:10.5007/1808-1711.2019v23n3p461
fatcat:4cwnzwvubzazbf2jep7aa7pnc4
Metaplectic geometrical optics for ray-based modeling of caustics: Theory and algorithms
[article]
2022
arXiv
pre-print
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Here, we overview the MGO theory and review algorithms that will aid the development of an MGO-based ray-tracing code. ...
By continuously adjusting the matrix coefficients and along the rays, one can ensure that GO remains valid in the X coordinates without caustic singularities. ...
Being singularities of a gradient map [Eq. (15b)], caustics are optical catastrophes 48 , and as such, they can be systematically classified using catastrophe theory 49 . ...
arXiv:2112.07399v3
fatcat:4ahweswn75fujl5pnf64c5345u
Spectra and Quantum Transport on Graphs
[chapter]
2018
Graph Theory - Advanced Algorithms and Applications
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We show how the notions, methods, and constructions of graph theory can help one to solve difficult problems, and also highlight recent developments in spectral theory of multiparticle random Hamiltonians ...
This chapter is devoted to various interactions between the graph theory and mathematical physics of disordered media, studying spectral properties of random quantum Hamiltonians. ...
Graph Theory -Advanced Algorithms and Applications ...
doi:10.5772/intechopen.68480
fatcat:4l5uhjcn3naabmjhbgptp4zju4
A Simple Algorithm for Calculating Electrical Double Layer Interactions in Asymmetric Electrolytes—Poisson–Boltzmann Theory
2002
Journal of Colloid and Interface Science
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A simple, general, and numerically robust algorithm is presented for calculating the disjoining pressure and interaction free energy per unit area between two identically charged flat plates due to electrical ...
double layer interactions according to the nonlinear Poisson-Boltzmann theory. ...
The nonlinear Poisson-Boltzmann theory provides an accurate mean field description of electrical double layer interactions in the colloidal regime and it is used extensively in interpreting direct and ...
doi:10.1006/jcis.2001.7942
pmid:16290364
fatcat:sll6p6i6nbgiteti6ybazjnl4m
On removal of charge singularity in Poisson–Boltzmann equation
2009
Journal of Chemical Physics
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The Poisson-Boltzmann theory has become widely accepted in modeling electrostatic solvation interactions in biomolecular calculations. ...
The proposed method can be readily implemented with typical finite-difference Poisson-Boltzmann solvers and return the singularity-free reaction field potential with a single run. ...
THEORY
A. ...
doi:10.1063/1.3099708
pmid:19368474
fatcat:hfbzllebtnd4ngweiphe3u3n3q
Discrete singular convolution and its application to computational electromagnetics
[article]
2000
arXiv
pre-print
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A Galerkin-induced collocation approach is used for a waveguide analysis in both regular and irregular domains and for electrostatic field estimation via potential functions. ...
A new computational algorithm, the discrete singular convolution (DSC), is introduced for computational electromagnetics. ...
Acknowledgment This work was supported in part by the National University of Singapore and in part by the National Science and Technology Board of the Republic of Singapore. ...
arXiv:math/0007113v1
fatcat:453agxl255afzepgiet5gsdste
Treatment of geometric singularities in implicit solvent models
2007
Journal of Chemical Physics
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and leads to highly accurate biomolecular electrostatics in continuum electric environments. ...
Converged electrostatic potentials and solvation free energies are obtained at a coarse grid spacing of 0.5 Å and are considerably more accurate than those obtained by the PBEQ and the APBS at finer grid ...
DMS-0616704 and IIS-0430987. The authors thank Yongcheng Zhou for useful discussions and Nathan Baker for valuable comments. ...
doi:10.1063/1.2743020
pmid:17614538
fatcat:qfnur6gdfzdephelun57n7mqqa
Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping
[article]
2019
arXiv
pre-print
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We first explain its loss of accuracy as panels become curved, using a classical complex approximation result of Walsh that can be interpreted as "electrostatic shielding" of a Schwarz singularity. ...
The method of Helsing and co-workers evaluates Laplace and related layer potentials generated by a panel (composite) quadrature on a curve, efficiently and with high-order accuracy for arbitrarily close ...
We gave a quantitative explanation for both the HO and SSQ convergence rates using classical polynomial approximation theory:
Acknowledgments The authors would like to thank Johan Helsing and Charlie ...
arXiv:1910.09899v1
fatcat:xjdcfx2dnrdohgx7xdzaghwirm
Treatment of charge singularities in implicit solvent models
2007
Journal of Chemical Physics
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Moreover, molecular surfaces admit geometric singularities, 40,42-44 such as cusps and self-intersecting surfaces. Explicit interface treatment of geometric singularities a͒ ...
The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2 Å for proteins. ...
Although a variety of methods, including Ewald summations, Euler summations, periodic images, and reaction field theory, have been developed in the past few decades, explicit electrostatic calculations ...
doi:10.1063/1.2768064
pmid:17887827
fatcat:usfqb4xo75celnf52rzl7ycszu
Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping
2020
BIT Numerical Mathematics
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We first explain its loss of accuracy as panels become curved, using a classical complex approximation result of Walsh that can be interpreted as "electrostatic shielding" of a Schwarz singularity. ...
The numerical method of Helsing and co-workers evaluates Laplace and related layer potentials generated by a panel (composite) quadrature on a curve, efficiently and with high-order accuracy for arbitrarily ...
The authors would like to thank Johan Helsing, Charlie Epstein, Ondrej Maxian, and Aleks Donev for fruitful discussions, and the anonymous referees for useful comments. ...
doi:10.1007/s10543-020-00820-5
fatcat:b2ug5mymuvcmxecppgzz6sj5eq
On the δ-singularities of the electromagnetic field
[article]
2010
arXiv
pre-print
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The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. ...
We show that for higher orders, it is more efficient to have fields represented in terms of symmetric and trace free moments. ...
Singularities of the electrostatic field Let us consider the multipole expansion of the electrostatic field derived from the potential expansion (6) in the static case: E(r) = 1 4πε 0 n≥0 (−1) n−1 n! ...
arXiv:1006.0696v1
fatcat:hapo7teibjaotdgavltrrkusme
Scalar waves on a naked-singularity background
2004
Classical and quantum gravity
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of the function spaces involved, show how to transform the problem to one about the wave equation on the Minkowski space with a singular potential, and finally prove that the potential thus obtained satisfies ...
We obtain global space-time weighted-L^2 (Morawetz) and L^4 (Strichartz) estimates for a massless chargeless scalar field propagating on a super-extremal (overcharged) Reissner-Nordstrom background. ...
The corresponding quantities in unrationalized electrostatic units e * and m * are related to e and m in the following way: m = G c 2 m * and e = √ G c 2 e * . ...
doi:10.1088/0264-9381/21/12/004
fatcat:zip5yuydorhyne4p2t35ngmuru
A fast and well-conditioned spectral method for singular integral equations
[article]
2016
arXiv
pre-print
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Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field ...
We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded ...
We acknowledge the generous support of the Natural Sciences and Engineering Research Council of Canada (RMS) and the Australian Research Council (SO). ...
arXiv:1507.00596v2
fatcat:n6r47hnkbreuhmgiw7hsusycla
Approximate Generalized Inverses with Iterative Refinement for ϵ-Accurate Preconditioning of Singular Systems
[article]
2021
arXiv
pre-print
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We introduce a new class of preconditioners to enable flexible GMRES to find a least-squares solution, and potentially the pseudoinverse solution, of large-scale sparse, asymmetric, singular, and potentially ...
We demonstrate the robustness of HIF and HIFIR and show that they improve both accuracy and efficiency of the prior state of the art by orders of magnitude for systems with up to a million unknowns. ...
The theory and algorithms described in this paper are extensible to complex matrices (by replacing transpose with conjugate transpose) and to m × n RDLS problems (by padding |m − n| zero rows or columns ...
arXiv:2009.01673v8
fatcat:63bjck5myngvhlcr4wuqp4brgq
A Singularity-Free Boundary Equation Method for Wave Scattering
2011
IEEE Transactions on Antennas and Propagation
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2010 pre-print arXiv:1002.3993v1 fatcat:hfikmubdnragde7o77hzm2ezwy
Traditional boundary integral methods suffer from the singularity of Green's kernels. ...
It can be generalized to 3D problems and to other classes of linear problems, including acoustics and elasticity. ...
Tsynkov for informative and illuminating discussions that helped to catalyze the research reported in the paper. I also thank P.-G. Martinsson and G. Rodin for helpful comments. ...
doi:10.1109/tap.2010.2096189
fatcat:37ns6jfoyzhb7gaanooivdb2mi
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