William Isaac Newman

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• Cornell University, Ph.D.
• Professor (Full) at University of California, Los Angeles

We develop a simple model for the kinematics of charged particles in regions of magnetic turbulence. We approximate the local magnetic field as smoothly varying in strength and direction, where adiabatic invariance prevails, or as presenting rapid changes in direction or ‘kinks’. Particles execute guiding centre gyromotion around a field line. Howe...

Newman et al. [Phys. Rev. E 86, 026103 (2012)] showed that points uniformly distributed as independent and identically distributed random variables with nearest-neighbor interactions form clusters with a mean number of three points in each. Here, we extend our analysis to higher dimensions, ultimately going to infinite dimensions, and we show that...

Collisionless N-body simulations over tens of millions of years are an important tool in understanding the early evolution of planetary systems. We first present a CUDA kernel for evaluating the gravitational acceleration of N bodies that is intended primarily for when N is less than several thousand. We then use the kernel with a variable-order, v...

We present and analyze the performance of a new algorithm for performing accurate simulations of the solar system when collisions between massive bodies and test particles are permitted. The orbital motion of all bodies at all times is integrated using a high-order variable-timestep explicit Runge–Kutta Nyström (ERKN) method. The variation in the t...

In nonrelativistic hydrodynamics and magnetohydrodynamics, conservative integration schemes for the fluid equations of motion are generally employed. The computed quantities, namely, the mass density, (vector) momentum density, and energy density, can readily be converted back into the primitive variables that define the problem, namely, the mass d...

Random events can present what appears to be a pattern in the length of peak-to-peak sequences in time series and other point processes. Previously, we showed that this was the case in both individual and independently distributed processes as well as for Brownian walks. In addition, we introduced the use of the discrete form of the Langevin equati...

Vladimir Isaakovich Keilis-Borok, emeritus Professor in Residence of Geophysics at the University of California, Los Angeles (UCLA), passed away on 19 October 2013, following a long illness. He was born on 31 July 1921 in Moscow.

We explore, via analytical and numerical methods, the Kelvin-Helmholtz (KH) instability in relativistic magnetized plasmas, with applications to astrophysical jets. We solve the single-fluid relativistic magnetohydrodynamic (RMHD) equations in conservative form using a scheme which is fourth order in space and time. To recover the primitive RMHD va...

We present, analyze, and test a multirate Störmer-based algorithm for integrating close encounters when performing N-body simulations of the Sun, planets, and a large number of test particles. The algorithm is intended primarily for accurate simulations of the outer solar system. The algorithm uses stepsizes H and hi, i = 1, ..., Np, where hi H and...

Precession of the orbit poles and spin poles for triaxial bodies, including the possibility of phase locking, is addressed here. We provide a simple derivation of the time-averaged gravitational potential and associated torque, thereby confirming the results of Gladman et al. (Gladman, B., Quinn, D., Nicholson, P., Rand, R. [1996]. Icarus 122, 166–...

Sixty years ago, it was observed that any independent and identically distributed (i.i.d.) random variable would produce a pattern of peak-to-peak sequences with, on average, three events per sequence. This outcome was employed to show that randomness could yield, as a null hypothesis for animal populations, an explanation for their apparent 3-year...

Continuum mechanics underlies many geological and geophysical phenomena, from earthquakes and faults to the fluid dynamics of the Earth. This interdisciplinary book provides geoscientists, physicists and applied mathematicians with a class-tested, accessible overview of continuum mechanics. Starting from thermodynamic principles and geometrical ins...

We explore, analytically and by numerical simulation, the evolution of the Kelvin-Helmholtz (KH) instability in a relativistic magnetized astrophysical jet. Our results successfully reproduce numerous magnetohydrodynamic features observed in relativistic astrophysical environments. The KH instability arises from a variation in flow speed orthogonal...

Precession of the equinoxes and of satellite orbits for axisymmetric bodies is a celebrated part of the classical and orbital mechanics literature. The theory underlying the behavior of triaxial bodies, particularly when synchronous phase locking is present, has proven to be difficult to evaluate and controversial. We perform a first-principles der...

It is shown that, contrary to common experience and opinion, the exact solutions to Schrödinger's equation in one dimension (or any similar ordinary linear second-order differential equation) can be numerically computed at a speed characterized by the variations of the potential function, i.e. at effectively the speed of solving Hamilton's equation...

Tidal energy dissipation has an influence upon the orientation of the spin pole of a satellite or planet, relative to its orbit pole. We examine several cases in which dissipation rates may be high enough to have measurable effect.

A record-breaking temperature is the highest or lowest temperature at a station since the period of time considered began. The temperatures at a station constitute a time series. After the removal of daily and annual periodicities, the primary considerations are trends (i.e., global warming) and long-range correlations. We first carry out Monte Car...

A record-breaking earthquake has a larger magnitude than any previous earthquake in the study region. A starting date and minimum magnitude must be specified. The first earthquake to satisfy this condition is by definition a record- breaking earthquake. The next record-breaking earthquake has a larger magnitude than the first and so forth. In this...

Record-breaking events generated by the dynamics of driven nonlinear threshold systems are extracted and analyzed. They are compared to the record-breaking events extracted from the sequences of independent identically distributed (i.i.d.) random variables drawn from the Weibull distribution. Several statistical measures of record-breaking events a...

Fiber bundle models (FBMs) are useful tools in understanding failure processes in a variety of material systems. While the fibers and load sharing assumptions are easily described, FBM analysis is typically difficult. Monte Carlo methods are also hampered by the severe computational demands of large bundle sizes, which overwhelm just as behavior re...

This work investigates the short wavelength stability of the magnetopause between a rapidly-rotating, supersonic, dense accretion disc and a slowly-rotating low-density magnetosphere of a magnetized star. The magnetopause is a strong shear layer with rapid changes in the azimuthal velocity, the density, and the magnetic field over a short radial di...

The ETAS (epidemic type aftershock sequence) model is an empirical simulation approach to aftershocks statistics. It is based on Gutenberg-Richter (GR) frequency-magnitude scaling and Omori's law for the temporal decay of aftershock sequences. In addition an empirical productivity law is postulated. The BASS (branching aftershock sequence) model is...

The optical, X-ray, and gamma-ray outbursts, as well as the associated formation of relativistically moving components of parsec-scale jets of some active galactic nuclei (AGNs) are interpreted as dynamical events in a magnetized accretion disk of a massive black hole. Here we discuss the theory and simulation results for a time-dependent, axisymme...

An intense localized magnetic field is suddenly introduced into a stationary, uniform, cold plasma and generates a region characterized by an intense field that excludes all particles ("magnetic bubble") enveloped by a spherical shell of very dense plasma ("snowplow"). Outside the shell, the field disappears over a small distance scale and the plas...

Tokunaga self-similar networks have a wide range of applications in the geosciences. The original application was to drainage networks. Tokunaga extended the Horton-Strahler length-order scaling of stream networks to include self-similar side branching. The addition of side branching provided important constraints on alternative models of river net...

Libration in the moon and other planets and satellites can be defined, after clarifying underlying geometrical issues, as a set of ordinary differential equations analogous to those for a spinning rigid body. We show the emergence of two conservation laws, and how one of these can be converted formally into a Hamiltonian whose dynamics explicitly r...

Record breaking events are analyzed in driven nonlinear threshold systems. These systems usually exhibit avalanche type behavior, where slow buildup of energy is punctuated by an abrupt release of energy through avalanche events which usually follow scale invariant statistics. During nonlinear dynamics of these system it is possible to extract a se...

A record-breaking event is the largest (smallest) event to occur during a specified time window in a specified region. In this paper we consider the record-breaking statistics of global earthquakes and temperatures at a specified observatory. For the record-breaking earthquakes we consider the global CMT catalog for the period 1977 to 2007. We dete...

A record-breaking earthquake has a magnitude larger than any previous earthquake. In order to constrain the problem, the region, starting time, and minimum magnitude must be specified. A remarkably simple theory is applicable if the earthquakes occur randomly. The mean number of record-breaking earthquakes is simply related to the natural logarithm...

The anelastic deformation of solids is often treated using continuum damage mechanics. An alternative approach to the brittle failure of a solid is provided by the discrete fibre-bundle model. Here we show that the continuum damage model can give exactly the same solution for material failure as the fibre-bundle model. We compare both models with l...

The purpose of this paper is to discuss the statistical distributions of recurrence times of earthquakes. Recurrence times are the time intervals between successive earthquakes at a specified location on a specified fault. Although a number of statistical distributions have been proposed for recurrence times, we argue in favor of the Weibull distri...

Manuscript consists of text (37 pages), 2 tables, and 10 figures.

The probabilistic theory of record-breaking was developed by Tata (1969), Nezvorov (1986) and others to describe the frequency of occurrence of record-breaking events in random trials. These results have been applied by Redner and Peterson (2006) in exploring the possible role of global warming on the statistics of record-breaking temperatures and...

The equations describing the dynamics of rotating bodies on precessing orbits are naturally treated in terms of geometric transformations (rotations) of the angular momentum vectors. Indeed, Cassini's (1693) well-known laws regarding rotation of synchronous bodies are not physical laws, but rather geometrical constraints. The physical basis for the...

Sussman and Wisdom [1992] found that the outer Solar System is chaotic with a Lyapunov time of seven to twenty million years. The shortness of this Lyapunov time stimulated research on the long-term behaviour of the outer Solar System. Three important results have emerged from this research. First, for long-term simulations using symplectic methods...

Apollo 14 breccia 14076 contains diverse silicate impact-vapor condensates: quenched-melt spheroids mostly <5 μm across, clasts up to 200 μm; all extremely low in refractory oxides. Spheroids have mg from 7-84 mol%, and FeO/SiO2 (wt.) from 0.002-0.67.

A Tokunaga fractal is a self-similar branching topology that includes both primary and side branching. It was developed in terms of the self-similar branching of stream networks. It was subsequently shown that the branching topology of diffusion limited aggregation (DLA) clusters is also a Tokunaga fractal. The epidemic type aftershock sequence (ET...

The statistical distribution of recurrence times of characteristic earthquakes plays an important role in hazard assessment. Assumed distributions include the exponential (random), Weibull (stretched exponential), log-normal, and Brownian passage time (inverse Gaussian). In this paper we argue that the Weibull distribution provides the proper scali...

SUMMARY The concept of self-organized complexity evolved from the scaling behaviour of several cellular automata models, examples include the sandpile, slider-block and forest-fire models. Each of these systems has a large number of degrees of freedom and shows a power-law frequency- area distribution of avalanches with N ∝ A−α and α ≈ 1. Actual la...

The numerical integration of Newton's equations of motion for self-gravitating systems, particularly in the context of our Solar System's evolution, remains a paradigm for complex dynamics. We implement Stormer's multistep method in backward difference, summed form and perform arithmetic according to a technique we call "significance ordered comput...

The integration of Newton’s equations of motion for self-gravitating systems, particularly in the context of our Solar System’s evolution, remains a paradigm for complex dynamics. We implement Störmer’s multistep method in backward difference, summed form and perform arithmetic according to what we call ‘significance ordered computation’. We achiev...

Symplectic integration methods are popular topics of investigation in numerical analysis and dynamical systems theory. In general, they do not produce trajectories corresponding to some approximate Hamiltonian (Varadarajan, 1973; Lichtenberg & Lieberman, 1992) but reside ``close" to some approximate Hamiltonian for a time determined by the time ste...

Gauge freedom emerges when the number of mathematical variables exceeds the number of physical degrees of freedom and, thus, generates a continuous group of physically-equivalent reparametrisations of the theory. This internal freedom may be interconnected with freedom of coordinate-frame choice (e.g., general relativity) or may be totally independ...

It is puzzling that certain brain tumors exhibit arrested exponential growth. We have observed in pediatric low-grade astrocytomas (LGA) at a certain volume approximately 100-150 cm(3) that the tumor ceases to grow. This observation led us to develop a macroscopic mathematical model for LGA growth kinetics that assumes the flow through the surface...

The method of variation of constants is an important tool used to solve systems of ordinary differential equations, and was invented by Euler and Lagrange to solve a problem in orbital mechanics. This methodology assumes that certain "constants" associated with a homogeneous problem will vary in time in response to an external force. It also introd...

We have studied a hybrid model combining the forest-fire model with the site-percolation model in order to better understand the earthquake cycle. We consider a square array of sites. At each time step, a "tree" is dropped on a randomly chosen site and is planted if the site is unoccupied. When a cluster of "trees" spans the site (a percolating clu...

We assess the principal statistical and physical uncertainties associated with the determination of magnetic field strengths in clusters of galaxies from measurements of Faraday rotation (FR) and Compton-synchrotron emissions. In the former case a basic limitation is noted, that the relative uncertainty in the estimation of the mean-squared FR will...

Symplectic integrators do not, in general, reproduce all the features of the dynamics of the Hamiltonian systems which they approximate. For example, energy conservation is lost, and global features such as separatrices can be destroyed. We study these effects for a Hamiltonian system with a single degree of freedom and the simplest possible symple...

The large-scale structure and dynamical evolution of the universe is modeled as a fluid, a good approximation for baryonic mass but possibly problematic for collisionless dark matter. The dynamical equations describing this self-gravitating system are scale-free allowing the spatial two-point statistics of galaxies to be a power-law. The observed v...

Complexity describes the transition from order to chaos, where nonlinear interactions inextricably link space and time, where the whole is greater than the sum of its parts. Complexity may be seen in patterns that can reproduce at different scales embracing a hierarchy of interactions, where fractal structures are often produced, yet preserving a s...

Fiber bundle models, where fibers have random lifetimes depending on their load histories, are useful tools in explaining time-dependent failure in heterogeneous materials. Such models shed light on diverse phenomena such as fatigue in structural materials and earthquakes in geophysical settings. Various asymptotic and approximate theories have bee...

Uniform scaling and renormalization of premonitory seismicity patterns is demonstrated in the models and data analysis. Patterns reflect four paradigms in earthquake prediction: (i) existence of several types of premonitory transformation of seismicity; (ii) long-range interactions; (iii) similarity; and (iv) dual origin of PSPs (partly "universal"...

A model of colliding cascades is developed. The model reflects the following relevant features of many complex systems: (i) hierarchical structure, (ii) direct cascade of loading due to external forces, (iii) inverse cascade of failures. We use the recently developed Boolean Delays concept to model the dynamics of colliding cascades. The model does...

A wide set of premonitory seismicity patterns is reproduced on a numerical model of seismicity, and their performance in the prediction of major model earthquakes is evaluated. Seismicity is generated by the colliding cascades model, recently developed by the authors. The model has a hierarchical structure. It describes the interaction of two casca...

We consider here the interaction of direct and inverse cascades in a hierarchical nonlinear system that is continuously loaded by external forces. The load is applied to the largest element and is transferred down the hierarchy to consecutively smaller elements, thereby forming a direct cascade. The elements of the system fail (i. e., break down) u...

Burgers equation is employed as a pedagogical device for analytically demonstrating the emergence of a form of inverse cascade to the lowest wavenumber in a flow. The transition from highly nonlinear mode-mode coupling to an ordered preference for large scale structure is shown, both analytically (revealing the presence of a global attractor) and v...

We determined analytically the dependence of the Lyapunov exponent upon time step for the linear paradigms of the simple harmonic oscillator (center) and simple repeller (homoclinic point) for several popular symplectic integration schemes. For the oscillator, we showed that there is a Hopf bifurcation resulting in the appearance of a non-zero Lyap...

Earthquakes occur on a hierarchy of faults in response to tectonic stresses. Earthquakes satisfy a variety of scaling relations; the most important is the Guttenberg-Richter frequency magnitude scaling. A variety of simple models have been shown to exhibit similar scaling. These models are said to exhibit self-organized criticality and one of the m...

We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how this model can provide a general explanation for the behavior of several models that has been described as "sel...

We report on numerical simulations designed to understand the distribution of small bodies in the Solar System and the winnowing of planetesimals accreted from the early solar nebula. The primordial planetesimal swarm evolved in a phase space divided into regimes by separatrices which define their trajectories and fate. This sorting process is driv...

We report on numerical simulations exploring the dynamical stability of planetesimals in the gaps between the outer Solar System planets. We search for stable niches in the Saturn/Uranus and Uranus/Neptune zones by employing 10,000 massless particles—many more than previous studies in these two zones—using high-order optimized multistep integration...

We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how this model can provide a general explanation for the behavior of several models that has been described as ``se...

We introduce an inverse-cascade model to explain self-organized critical behavior. This model is motivated by the forest-fire model. In the forest-fire model trees are randomly planted on a grid, sparks are also dropped on the grid resulting in fires in which trees are lost. In the inverse-cascade model single trees are introduced and these combine...

We investigate a parametrically excited nonlinear Mathieu equation with damping and limited spatial dependence, using both perturbation theory and numerical integration. The perturbation results predict that, for parameters which lie near the 2:1 resonance tongue of instability corresponding to a single mode of shape cos nx, the resonant mode ac...

We have investigated by analytical and computational means the effect of Cretaceous–Tertiary (K/T) size impacts (5×1030erg, 9-km-radius bolide of 1019g) on terrestrial atmospheres. We have extended analytically the approximate solution due to A. S. Kompaneets (1960,Sov. Phys. Dokl. Engl. Transl.5, 46–48) for the blast wave obtained for atmospheric...

Last year, Kouveliotou et al. (1998) discovered a new class of short-lived old stellar objects known as magnetars. When a massive star undergoes the catastrophic collapse which precedes a supernova explosion, it undergoes a very rapid spin-up causing its attached dipolar magnetic field lines to become very tightly wound in a toroidal configuration...

There are many examples of branching networks in biology. Examples include the structure of plants and trees as well as cardiovascular and bronchial systems. In many cases these networks are self-similar and exhibit fractal scaling. In this paper we introduce the Tokunaga taxonomy for the side branching of networks and his parameterization of self-...

Symplectic mapping techniques have become very popular among celestial mechanicians and molecular dynamicists. The word "symplectic" was coined by Hermann Weyl (1939), exploiting the Greek root for a word meaning "complex," to describe a Lie group with special geometric properties. A symplectic integration method is one whose time-derivative satisf...

Accurate modeling of close planet/planetesimal approaches has become an increasingly important topic in planetary dynamical simulations (Newman et al., 1997; Levison, 1997; Grazier, 1997; Rauch and Holman, 1998). Using the Newton backwards difference interpolation formula, coupled to our modified Stormer integrator, we present a new, accurate, data...

Most of the marked differences in Venus from Earth can be attributed to evolutionary circumstances, particularly those arising from a deficiency of water in Venus' outer layers. But three major differences depend on circumstances of origin: (1) the absence of a magnetic field; (2) the retrograde spin and, thence, no satellite; and (3) the greater a...

This paper considers fractal trees with self-similar side branching. The Tokunaga classification system for side branching is introduced, along with the Tokunaga self-similarity condition. Area filling (D = 2) and volume filling (D = 3) deterministic fractal tree constructions are introduced both with and without side branching. Applications to dif...

: We analyze the ion concentrations of groundwater issuing from deep wells located near the epicenter of the recent earthquake of magnitude 6:9 near Kobe, Japan, on January 17, 1995. These concentrations are well fitted by log-periodic modulations around a leading power law. The exponent (real and imaginary parts) is very close to those already fou...

Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth's topography is an example of both statistically self-similar and s...

The Ar-36+38 argon-excess anomally of Venus has been hypothesized to have its origin in the impact of an outer solar system body of about 100-km diameter. A critical evaluation is made of this hypothesis and its competitors; it is judged that its status must for the time being remain one of 'Sherlock Holmes' type, in that something so improbable mu...

We provide a formal mathematical analysis of the “Power Spectrum Analysis” (PSA) method by Yu and Peebles (1969), including illustrative controlled numerical experiments, to better understand their properties. The PSA method generates a sequence of random numbers from observational data which, it was claimed, is exponentially distributed with unit...

We investigate the evolution of the atmospheric blast waves produced by a K-T sized meteoritic impact on a terrestrial planet. Extending the mathematical analysis due to Kompaneets (1960) for a localized explosion in an isothermal atmosphere, we explore the response of an adiabatic atmosphere as well as model atmospheres for Earth and Venus to a 5...

Seismic activation has been recognized to occur before many major earthquakes including the San Francisco Bay area, prior to the 1906 earthquake. There is a serious concern that the recent series of earthquakes in Southern California is seismic activation prior to a great Southern California earthquake. The seismic activation prior to the Loma Prie...

We investigate a nonlinear Mathieu equation with diffusion and damping, using both perturbation theory and numerical integration. The perturbation results predict that for parameters which lie near the 2 : 1 resonance tongue of instability corresponding to a mode shape cos nx the resonant mode achieves a stable periodic motion, while all the other...

The relationship between symplectic properties and numerical accuracy is investigated using the dynamics of the Jovian planets as an example. What are the properties of symplectic integrators, including both their benefits and limitations, and how do they contrast with classical integration schemes? The dynamics of the Wisdom-Holman mapping appears...

Using high-order multistep integration methods optimized to minimize roundoff error propagation, we performed fully three-dimensional integrations of planetesimal trajectories for 100 million years to examine possible niches in the Jupiter/Saturn, Saturn/Uranus, and Uranus/Neptune zones. We computed the trajectories of 100,000 massless particles in...

Arp (1994) has presented redshift data for the Local Group of galaxies and for the next major group, whose largest galaxies are M31 and M81, respectively. He observed that the relative redshifts of all 22 of their companions were positive and claimed that the likelihood that this would occur is 1 in 4 x 10(exp 6). We show using the classical combin...

In this paper, the authors show how the variability of the water content in individual clouds, the complexity of individual cloud structure, and the lateral and vertical heterogeneity of the distribution of individual clouds can produce systematic effects in the inversion of intensity distributions and the inference of source functions and the vert...

A model and simulation code have been developed for time-dependent axisymmetric disk accretion onto a compact object including for the first time the influence of an ordered magnetic field. The accretion rate and radiative luminosity of the disk are naturally coupled to the rate of outflow of energy and angular momentum in magnetically driven (+/-...