Tony Scott
RWTH Aachen University, Institute of Physical Chemistry, Department Member
- Tony C. Scott graduated in 1991 with a Ph.D. in Theoretical Physics and wasawarded the Pearson Medal for best Physics... moreTony C. Scott graduated in 1991 with a Ph.D. in Theoretical Physics and wasawarded the Pearson Medal for best Physics Doctoral thesis at the Universityof Waterloo (1991). His Masters thesis in Applied Mathematics (1986) is cited in the wikipedia section on the Wheeler-Feynman absorber theory. Awarded with an N.S.E.R.C. postdoctoral scholarship, he subsequently did research in Mathematical Physics at the Harvard-Smithsonian in Cambridge MA USA ('90-'92). Afterwards, he did research in relativistic quantum chemistry and pioneered a mathematics course using computer algebra at the Mathematical institute in Oxford University in the UK ('93-'95). This was followed by further work at the University of Ben-Gurion in Israel ('96-'97), INRIA in France ('98-'99), the Forschungszentrum in Juelich Germany (2003) and eventually RWTH-Aachen University Germany (2003-2006) where he retains an affiliation. He worked for 7 years as a Data Scientist in Silicon Valley in the San Francisco bay area before returning as a professor in China. He is now back in the privatesector as a Data Scientist.His publications, patents, projects, etc...can be seen (and downloaded) from: https://www.researchgate.net/profile/Tony-Scott-2edit
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Herein, we use Hardy's notion of the "false derivative" to obtain exact multiple roots in closed form of the transcendental-algebraic equations representing the generalized Lambert W function. In this fashion, we flesh out... more
Herein, we use Hardy's notion of the "false derivative" to obtain exact multiple roots in closed form of the transcendental-algebraic equations representing the generalized Lambert W function. In this fashion, we flesh out the generalized Lambert W function by complementing previous developments to produce a more complete and integrated body of work. Finally, we demonstrate the usefulness of this special function with some applications.
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Unsupervised machine learning applied to the study of phase transitions is an ongoing and interesting research direction. The active contour model, also called the snake model, was initially proposed for target contour extraction in... more
Unsupervised machine learning applied to the study of phase transitions is an ongoing and interesting research direction. The active contour model, also called the snake model, was initially proposed for target contour extraction in two-dimensional images. In order to obtain a physical phase diagram, the snake model with an artificial neural network is applied in an unsupervised learning way by the authors of [Phys. Rev. Lett. 120, 176401 (2018)]. It guesses the phase boundary as an initial snake and then drives the snake to convergence with forces estimated by the artificial neural network. In this work we extend this unsupervised learning method with one contour to a snake net with multiple contours for the purpose of obtaining several phase boundaries in a phase diagram. For the classical Blume-Capel model, the phase diagram containing three and four phases is obtained. Moreover, a balloon force is introduced, which helps the snake to leave a wrong initial position and thus may allow for greater freedom in the initialization of the snake. Our method is helpful in determining the phase diagram with multiple phases using just snapshots of configurations from cold atoms or other experiments without knowledge of the phases.
Herein, it is shown that Kepler's contribution involving the "Music of the Spheres" can be traced back to Pythagoras and Ibn Arabī through Michael Scot. We find threads linking this body of work associating music with astronomy leading to... more
Herein, it is shown that Kepler's contribution involving the "Music of the Spheres" can be traced back to Pythagoras and Ibn Arabī through Michael Scot. We find threads linking this body of work associating music with astronomy leading to the modern and extensive astronomical subject of orbital resonances. In particular, we find that Fibonacci numbers play a significant role in this context.
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Keiper [1] and Li [2] published independent investigations of the connection between the Riemann hypothesis and the properties of sums over powers of zeros of the Riemann zeta function. Here we consider a reframing of the criterion, to... more
Keiper [1] and Li [2] published independent investigations of the connection between the Riemann hypothesis and the properties of sums over powers of zeros of the Riemann zeta function. Here we consider a reframing of the criterion, to work with higher-order derivatives xi_r of the symmetrized function xi(s) at s = 1/2, with all xi_r known to be positive. The reframed criterion requires knowledge of the asymptotic properties of two terms, one being an infinite sum over the xi_ r. This is studied using known asymptotic expansions for the xi_ r , which give the location of the summand as a relationship between two parameters. This relationship needs to be inverted, which we show can be done exactly using a generalized Lambert function. The result enables an accurate asymptotic expression for the value of the infinite sum.
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Research Interests: Computer Science, Information Technology, Data Mining, Computer Security, Cluster Analysis (Multivariate Data Analysis), and 10 moreOptimization, Big Data, Cluster Analysis, Data Clustering, Gaussian, Information Technology and System Integration, Deutsch's Quantum Algorithm, Energy function, Quantum clustering, and exponential polynomial
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It is shown that Symbolic Computation provides excellent tools for solving quantum mechanical problems by perturbation theory. The method presented herein solves for both the eigenfunctions and eigenenergies as power series in the order... more
It is shown that Symbolic Computation provides excellent tools for solving quantum mechanical problems by perturbation theory. The method presented herein solves for both the eigenfunctions and eigenenergies as power series in the order parameter where each coefficient of the perturbation series is obtained in closed form. The algorithms are expressed in the Maple symbolic computation system but can be implemented on other systems. This approach avoids the use of an infinite basis set and some of the complications of degenerate perturbation theory. It is general and can, in principle, be applied to many separable systems.
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It is shown that the Fokker–Wheeler–Feynman theory for the relativistic modelling of a system of massive, charged, point particles interacting via action-at-a-distance forces, electromagnetic in origin, can be reformulated and... more
It is shown that the Fokker–Wheeler–Feynman theory for the relativistic modelling of a system of massive, charged, point particles interacting via action-at-a-distance forces, electromagnetic in origin, can be reformulated and reinterpreted so that it retains all of its required physical attributes but is devoid of the absurdities originally ascribed to it. That is, Lorentz covariance, time-reversal symmetry, and particle-interchange symmetry are maintained, whereas lack of causality and the paradox of "discontinuous" forces are removed. The reformulated theory yields a physically acceptable relativistic, many-particle Lagrangian. The Euler–Lagrange equations of motion can be written down for either closed or open systems. For closed systems, a generalized Hamiltonian, linear momentum, and angular momentum are constants of the motion. The concept of an open system is used to show that radiation reaction follows straightforwardly from the Euler–Lagrange equations of motion and their past and present time solutions. It is concluded that the basis for this type of modelling of such systems is now established.
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ABSTRACT
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It is shown that Symbolic Computation provides excellent tools for solving quantum mechanical problems by perturbation theory. The method presented herein solves for both the eigenfunctions and eigenenergies as power series in the order... more
It is shown that Symbolic Computation provides excellent tools for solving quantum mechanical problems by perturbation theory. The method presented herein solves for both the eigenfunctions and eigenenergies as power series in the order parameter where each coefficient of the perturbation series is obtained in closed form. The algorithms are expressed in the Maple symbolic computation system but can be implemented on other systems. This approach avoids the use of an infinite basis set and some of the complications of degenerate perturbation theory. It is general and can, in principle, be applied to many separable systems.
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Research Interests:
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By using the density matrix renormalization group and mean field methods, the anyon Hubbard model is studied systematically on a one dimensional lattice. The model can be expressed as a Bose-Hubbard model with a density-dependent-phase... more
By using the density matrix renormalization group and mean field methods, the anyon Hubbard model is studied systematically on a one dimensional lattice. The model can be expressed as a Bose-Hubbard model with a density-dependent-phase term. When the phase angle is $\theta=0$ or $\theta=\pi$, the model will be equivalent to boson and pseudo fermion models, respectively. In the mean field frame, we find a broken-symmetry superfluid (BSF), in which the $b^{\dagger}(b)$ operators on the nearest neighborhood sites have exactly opposite directions and behave like a directed oscillation pattern. By the density matrix reorganization group method, in the broken-symmetry superfluid, both the real and imaginary parts of the correlation $b^{\dagger}_ib_{i+r}$ behave according to a {\it beat phenomenon} with $0<\theta<\pi$ in the form $C_0e^{i k r}(-1)^{r}$ or behave like waves with different wavelengths in the form $C_0e^{i k r}$. The distributions of the broken-symmetry superfluid phase...
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Herein is a review of the essentials of Modified Newtonian Dynamics (MOND) versus dark matter models based on Superfluids for modeling galactic rotation curves. We review the successes and issues of both approaches. We then mention a... more
Herein is a review of the essentials of Modified Newtonian Dynamics (MOND) versus dark matter models based on Superfluids for modeling galactic rotation curves. We review the successes and issues of both approaches. We then mention a recent alternative based on the Superfluid Vacuum Theory (SVT) with a nonlinear logarithmic Schrödinger equation (LogSE) which reconciles both approaches, retains the essential success of MOND and the Superfluid nature but does not necessitate the hypothesis of processes including dark matter. We conclude with the implications of this SVT alternative on quantum theory itself.
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Some form of the time-independent logarithmic Schrödinger equation (log SE) arises in almost every branch of physics. Nevertheless, little progress has been made in obtaining analytical or numerical solutions due to the nonlinearity of... more
Some form of the time-independent logarithmic Schrödinger equation (log SE) arises in almost every branch of physics. Nevertheless, little progress has been made in obtaining analytical or numerical solutions due to the nonlinearity of the logarithmic term in the Hamiltonian. Even for a central potential, the Hamiltonian does not commute with L 2 or L z ; the Hamiltonian is invariant under the parity operation only if the wave function is an eigenstate of the parity operator. We show that the solutions with well-defined parity can be expressed as a linear combination of eigenstates of L 2 and L z , where the parity restrictions on l and m determine the nodal structure of the wave function. The dominant contribution in the sum is designated as l ˜ and m ˜ ; these serve as approximate quantum numbers. Using an iterative finite element approach, we also carry out fully converged numerical calculations in 1D, 2D and 3D for the special case of a Coulomb potential. The nodal structure of ...
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We apply a physical and historical analysis to a passage by the medieval scholar Michael Scot concerning multiple rainbows, a meteorological phenomenon whose existence has only been acknowledged in recent history. We survey various types... more
We apply a physical and historical analysis to a passage by the medieval scholar Michael Scot concerning multiple rainbows, a meteorological phenomenon whose existence has only been acknowledged in recent history. We survey various types of physical models to best decipher Scot’s description of four parallel rainbows as well as a linguistic analysis of Scot’s special etymology. The conclusions have implications on Scot’s whereabouts at the turn of the 13th century.
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Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a σ value, a hyper-parameter which can be... more
Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a σ value, a hyper-parameter which can be manually defined and manipulated to suit the application. Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an outstanding task because normally such expressions are impossible to solve analytically. However, we prove that if the points are all included in a square region of size σ, there is only one minimum. This bound is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new numerical approach “per block”. This technique decreases the number of p...
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Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a 𝜎 value, a hyper-parameter which can be... more
Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a 𝜎 value, a hyper-parameter which can be manually defined and manipulated to suit the application. Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an outstanding task because normally such expressions are impossible to solve analytically. However, we prove that if the points are all included in a square region of size 𝜎, there is only one minimum. This bound is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new numerical approach “per block”. This technique decreases the number of p...
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Research Interests:
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of... more
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of expressing solutions to a number of physical problems of fundamental nature. In particular, this generalization expresses the exact solutions for general-relativistic self-gravitating 2-body and 3-body systems in one spatial and one time dimension. It also expresses the solution to a previously unknown mathematical link between the lineal gravity problem and the Schroedinger equation.
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Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of... more
Herein, we present a canonical form for a natural and necessary generalization of the Lambert W function, natural in that it requires minimal mathematical definitions for this generalization, and necessary in that it provides a means of expressing solutions to a number of physical problems of fundamental nature. In particular, this generalization expresses the exact solutions for general-relativistic self-gravitating 2-body and 3-body systems in one spatial and one time dimension. It also expresses the solution to a previously unknown mathematical link between the lineal gravity problem and the Schroedinger equation.
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Research Interests:
Experimental data suggests that, at temperatures below 1 K, the pressure in liquid helium has a cubic dependence on density. Thus the speed of sound scales as a cubic root of pressure. Near a critical pressure point, this speed approaches... more
Experimental data suggests that, at temperatures below 1 K, the pressure in liquid helium has a cubic dependence on density. Thus the speed of sound scales as a cubic root of pressure. Near a critical pressure point, this speed approaches zero whereby the critical pressure is negative, thus indicating a cavitation instability regime. We demonstrate that to explain this dependence, one has to view liquid helium as a mixture of three quantum Bose liquids: dilute (Gross-Pitaevskii-type) Bose-Einstein condensate, Ginzburg-Sobyanin-type fluid, and logarithmic superfluid. Therefore, the dynamics of such a mixture is described by a quantum wave equation, which contains not only the polynomial (Gross-Pitaevskii and Ginzburg-Sobyanin) nonlinearities with respect to a condensate wavefunction, but also a non-polynomial logarithmic nonlinearity. We derive an equation of state and speed of sound in our model, and show their agreement with the experiment.
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... ET LA PAPERS THE AUTHORS Biographies of Drs. Lipshitz published in the March issue. and Vanderkooy were Shift 00M[t] to the time left by AT; (negative ie set: direction) T = x - AT TonyScott graduated from the University of Waterloo... more
... ET LA PAPERS THE AUTHORS Biographies of Drs. Lipshitz published in the March issue. and Vanderkooy were Shift 00M[t] to the time left by AT; (negative ie set: direction) T = x - AT TonyScott graduated from the University of Waterloo in 1984 with a B.Sc. (honors) in physics. ...
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... He has consuited for a number of companies on audio-related questions. Tony Scott has a background in physics, applied mathematics, and computer algebra, and obtained a doctoral degree in 1990 from the University of Waterloo. ... Tony... more
... He has consuited for a number of companies on audio-related questions. Tony Scott has a background in physics, applied mathematics, and computer algebra, and obtained a doctoral degree in 1990 from the University of Waterloo. ... Tony Scott's time. ...
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Research Interests:
ABSTRACT
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Herein, we present a sequel to earlier work on a generalization of the Lambert W function. In particular, we examine series expansions of the generalized version providing computational means for evaluating this function in various... more
Herein, we present a sequel to earlier work on a generalization of the Lambert W function. In particular, we examine series expansions of the generalized version providing computational means for evaluating this function in various regimes and further confirming the notion that this generalization is a natural nextension of the standard Lambert W function.
Compendium and update of several conferences and papers on the Wheeler-Feynman Time-Symmetric Theory plus materials and a few notions related to these presentations.