Prof. Bruce Boghosian

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Academic Career Length

27Years (2000-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

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30 June 2010 in Physical Review Letters

Journal Article

Fast Lattice Boltzmann Solver for Relativistic Hydrodynamics

Miller Mendoza Jimenez

Bruce Boghosian

H. J. Herrmann

Sauro Succi

A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows.

14 August 2015 in Journal of Statistical Physics

Journal Article

An H Theorem for Boltzmann’s Equation for the Yard-Sale Model of Asset Exchange

Bruce Boghosian

Merek Johnson

Jeremy A. Marcq

In recent work (Boghosian, Phys Rev E 89:042804–042825, 2014 ; Boghosian, Int J Mod Phys 25:1441008–1441015, 2014 ), Boltzmann and Fokker–Planck equations were derived for the “Yard-Sale Model” of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy—complete concentration of wealth by a single individual. In this work, we prove that conjecture by demonstrating that the Gini coefficient, a measure of inequality commonly used by economists, is an H function of both the Boltzmann and Fokker–Planck equations for the model.

10 November 2010 in Physical Review D

Journal Article

Derivation of the lattice Boltzmann model for relativistic hydrodynamics

Miller Mendoza Jimenez

Bruce Boghosian

H. J. Herrmann

Sauro Succi

A detailed derivation of the lattice Boltzmann scheme for relativistic fluids recently proposed in M. Mendoza, B. Boghosian, H. Herrmann, and S. Succi, Phys. Rev. Lett. 105, 014502 (2010) is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid-dynamic problems, namely, shock-wave propagation in quark-gluon plasmas and the impact of a supernova blast wave on massive interstellar clouds. Close to second-order convergence with the grid resolution, as well as linear dependence of computational time on the number of grid points and time steps, are reported.

23 September 2019 in Advanced Theory and Simulations

Journal Article

A New Pathology in the Simulation of Chaotic Dynamical Systems on Digital Computers

Bruce Boghosian

Peter V. Coveney

Hongyan Wang

Systematic distortions are uncovered in the statistical properties of chaotic dynamical systems when represented and simulated on digital computers using standard IEEE floating‐point numbers. This is done by studying a model chaotic dynamical system with a single free parameter β, known as the generalized Bernoulli map, many of whose exact properties are known. Much of the structure of the dynamical system is lost in the floating‐point representation. For even integer values of the parameter, the long time behaviour is completely wrong, subsuming the known anomalous behaviour for β = 2. For non‐integer β, relative errors in observables can reach 14%. For odd integer values of β, floating‐point results are more accurate, but still produce relative errors two orders of magnitude larger than those attributable to roundoff. The analysis indicates that the pathology described, which cannot be mitigated by increasing the precision of the floating point numbers, is a representative example of a deeper problem in the computation of expectation values for chaotic systems. The findings sound a warning about the uncritical application of numerical methods in studies of the statistical properties of chaotic dynamical systems, such as are routinely performed throughout computational science, including turbulence and molecular dynamics.

17 July 2001 in Physical Review E

Journal Article

Three-dimensional hydrodynamic lattice-gas simulations of domain growth and self-assembly in binary immiscible and ternary amphiphilic fluids

Peter J. Love

Peter V. Coveney

Bruce Boghosian

We simulate the dynamics of phase assembly in binary immiscible fluids and ternary microemulsions using a three-dimensional hydrodynamic lattice-gas approach. For critical spinodal decomposition we perform the scaling analysis in reduced variables introduced by Jury et al. [Phys. Rev. E 59, R2535 (1999)] and by Bladon et al. [Phys. Rev. Lett. 83, 579 (1999)]. We find a late-stage scaling exponent consistent with the

R \sim t^{2 / 3}

inertial regime. However, as observed with the previous lattice-gas model of Appert et al. [J. Stat. Phys. 81, 181 (1995)] our data do not fall in the same range of reduced length and time as those of Jury et al. and Bladon et al. For off-critical binary spinodal decomposition we observe a reduction of the effective exponent with decreasing volume fraction of the minority phase. However, the

n = \frac{1}{3}

Lifshitz-Slyzov-Wagner droplet coalescence exponent is not observed. Adding a sufficient number of surfactant particles to a critical quench of binary immiscible fluids produces a ternary bicontinuous microemulsion. We observe a change in scaling behavior from algebraic to logarithmic growth for amphiphilic fluids in which the domain growth is not arrested. For formation of a microemulsion where the domain growth is halted we find that a stretched exponential growth law provides the best fit to the data.

2 July 2004 in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Journal Article

Entropic lattice Boltzmann model for Burgers's equation

Bruce Boghosian

Peter Love

Jeffrey Yepez

Entropic lattice Boltzmann models are discrete–velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for the Navier—Stokes equations in two and three dimensions, and have been proposed as a new category of subgrid model of turbulence. In the present work we develop an entropic lattice Boltzmann model for Burgers's equation in one spatial dimension. In addition to its pedagogical value as a simple example of such a model, our result is actually a very effective way to simulate Burgers's equation in one dimension. At moderate to high values of viscosity, we confirm that it exhibits no trace of instability. At very small values of viscosity, however, we report the existence of oscillations of bounded amplitude in the vicinity of the shock, where gradient scale lengths become comparable with the grid size. As the viscosity decreases, the amplitude at which these oscillations saturate tends to increase. This indicates that, in spite of their nonlinear stability, entropic lattice Boltzmann models may become inaccurate when the ratio of gradient scale length to grid spacing becomes too small. Similar inaccuracies may limit the utility of the entropic lattice Boltzmann paradigm as a subgrid model of Navier—Stokes turbulence.

About Me

Bruce M. Boghosian holds a BS and an MS from MIT and a Ph.D. from the University of California, Davis. He is the sixth president of the American University of Armenia (AUA) in Yerevan, Armenia, having assumed that position in September 2023. He also served as that institution’s third president from 2010 to 2014. He has been a Professor of Mathematics at Tufts University since 2000, and served as chair of Mathematics there from 2006 to 2010. He also holds secondary faculty appointments in the Tufts University Departments of Physics and Computer Science. He has been a fellow of the American Physical Society since 2000, a recipient of Tufts University’s Distinguished Scholar Award in 2010, a foreign member of the National Academy of Sciences of the Republic of Armenia since 2008, a recipient of the “Order of the Republic of Armenia” from the Prime Minister of the Republic of Armenia in 2014, a recipient of the “Gold Medal” from the Ministry of Education and Science in the Republic of Armenia in 2014, a Fellow of the Jonathan M. Tisch College of Civic Life at Tufts University in 2018, and a Fellow of the Data Intensive Studies Center at Tufts University since 2020. His interests include mathematical fluid dynamics and kinetic theory, and, more recently, the application of these disciplines to problems in the social sciences, including wealth distribution, wealth inequality, the onset of oligarchy, and opinion dynamics.

Prof. Bruce Boghosian

Prof. Bruce Boghosian

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