# Adam Landsberg

### Professor of Physics

Email: alandsberg@kecksci.claremont.edu

Office: Keck Science Center 112

Phone: 909-607-8016

**Educational Background**

B.A., Princeton University

M.A., University of California, Berkeley

Ph.D., University of California, Berkeley

**Research Interests**

Applied Mathematics/Scientific Modeling of Complex Systems: networks, game theory, chaos, pattern formation, human-brain networks, self-organized criticality, economic and queuing systems, fluids, superconductors, solar cycles, etc.

**Thesis Topics**

Interested students should contact Prof. Landsberg for a description of current thesis topics this semester.

**Selected Publications**

- (2020). Transitioning Out of the Coronavirus Lockdown: A Framework for Evaluating Zone-Based Social Distancing.
*Frontiers in Public Health,*https://doi.org/10.3389/fpubh.2020.00266**:**(with Eric Friedman, John Friedman, Simon Johnson).**Abstract**– In the face of elevated pandemic risk, canonical epidemiological models imply the need for extreme social distancing over a prolonged period. Alternatively, people could be organized into zones, with more interactions inside their zone than across zones. Zones can deliver significantly lower infection rates, with less social distancing, particularly if combined with simple quarantine rules and contact tracing. This paper provides a framework for understanding and evaluating the implications of zones, quarantines, and other complementary policies. - (2020). Modeling Cultural Dissemination and Divergence Between Rural and Urban Regions.
*Journal of Artificial Societies and Social Simulation (with Nicholas LaBerge, Aria Chaderjian, Victor Ginellie, Margrethe Jebsen)*To appear: Vol. 23, Issue 4, 2020. - (2019). Geometric Analysis of a Generalized Wythoff Game.
*Games of No Chance 5, MSRI Publications vol. 70, Cambridge University Press*(with Eric Friedman, Scott Garrabrant, Ilona Phipps-Morgan, and Urban Larsson). - (2018). Duality and Nonlinear Graph Laplacians.
*Theoretical Computer Science*(with E. Friedman). Available online 28 Dec. 2017; https://doi.org/10.1016/j.tcs.2017.12.034. - (2015). Edge Correlations in Spatial Networks.
*Journal of Complex Networks***DOI: 10.1093/comnet/cnv015:**(with E. Friedman, J. Owen, W. Hsieh, L. Kam, P. Mukherjee). - (2015). Directed Network Motifs in Alzheimer’s Disease and Mild Cognitive Impairment.
*PLoS One***DOI: 10.1371/journal.pone.0124453 :**with E. Friedman, K. Young, G. Tremper, J. Liang, N. Schuff. - (2014). Directed Progression Brain Networks in Alzheimer’s Disease: Properties and Classification.
*Brain Connectivity***4(5), 384-393:**E. Friedman, K. Young, D. Asif, I. Jutla, M. Liang S. Wilson, N. Schuff. - (2014). Stochastic Geometric Network Models for Groups of Functional and Structural Connectomes.
*NeuroImage***101:**(with E. Friedman, J. Owen, Y. Li, P. Mukherjee). - (2013). Hierarchical networks, power laws, and neuronal avalanches.
*CHAOS***23 (1):**013135 (with E.J. Friedman).

Article (PDF) - (2013). Cofinite Induced Subgraphs of Impartial Combinatorial Games: An Analysis of CIS-Nim.
*INTEGERS***13:**(with Scott M. Garrabrant, Eric J. Friedman).

Article - (2011). Combinatorial games with a pass: A dynamical systems approach.
*CHAOS***043108:**(with Rebecca E. Morrison, Eric J. Friedman).**Abstract**– By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a pass move into a game affects its behavior. We consider two well known combinatorial games, 3-pile Nim and 3-row Chomp. In the case of Nim, we observe that the introduction of the pass dramatically alters the game’s underlying structure, rendering it considerably more complex, while for Chomp, the pass move is found to have relatively minimal impact. We show how these results can be understood by recasting these games as dynamical systems describable by dynamical recursion relations. From these recursion relations, we are able to identify underlying structural connections between these games with passes and a recently introduced class of generic (perturbed) games. This connection, together with a (non-rigorous) numerical stability analysis, allows one to understand and predict the effect of a pass on a game. VC 2011 American Institute of Physics. [doi:10.1063/1.3650234]**Article – URL not found** - E.J. Friedman and A.S. Landsberg. (2009). On the Geometry of Combinatorial Games: a Renormalization Approach.
*(MSRI series)*R. Nowakowski, ed. Cambridge University Press.

Article – URL not found - M. Furi, A.S. Landsberg AS, and M. Martelli. (2009). On the Longitudinal Librations of Hyperion.
*Journal of Fixed Point Theory and its Applications***:**1661-7738.**Article – URL not found** - Eric J. Friedman and Adam S. Landsberg. (2009). Construction and Analysis of Random Networks with Explosive Percolation.
*Physical Review Letters***103:**255701.

Article - E.J. Friedman and A.S. Landsberg. (2007). Nonlinear dynamics in combinatorial games: Renormalizing Chomp.
*Chaos***17:**023117.**Article – URL not found** - E.J. Friedman and A.S. Landsberg. (2007). Scaling, Renormalization, and Universality in Combinatorial Games.
*in Combinatorial Optimization and Applications*A. Dress et al., eds., Springer-Verlag. - M. Furi, A.S. Landsberg AS, and M. Martelli. (2005). On the chaotic behavior of the satellite hyperion.
*J. of Difference Eqns. and Applications***11 (7):**635-643.**Article – URL not found** - R. Gann*, J. Venable*, E.J. Friedman, and A.S. Landsberg. (2004). The Behavior of Coupled Automata.
*Physical Review E***69:**046116.

Abstract – We study the nature of statistical correlations that develop between systems of interacting self-organized critical automata (sandpiles). Numerical and analytical findings are presented describing the emergence of “synchronization” between sandpiles and the dependency of this synchronization on factors such as variations in coupling strength, toppling rule probabilities, symmetric versus asymmetric coupling rules, and numbers of sandpiles.**Article – URL not found** - E.J. Friedman, S. Johnson and A.S. Landsberg. (2003). The Emergence of Temporal Correlations in a Study of Global Economic Interdependence.
*Quantitative Finance***3:**296.

Abstract – We develop a simple firm-based automaton model for global economic interdependence of countries using modern notions of self-organized criticality and recently developed dynamical renormalization-group methods. We demonstrate how extremely strong statistical correlations can naturally develop between two countries even if the financial interconnections between those countries remain very weak. Potential policy implications of this result are also discussed.**Article – URL not found** - M. Crescimanno and A.S. Landsberg. (2001). Spectral Equivalence of Bosons and Fermions in One-Dimensional Harmonic Potentials.
*Physical Review A***64:**035601.

Abstract – Recently, Schmidt and Schnack [Physica A 260, 479 (1998)], following earlier references, reiterate that the specific heat of N noninteracting bosons in a one-dimensional harmonic well equals that of N noninteracting fermions in the same potential. We show that this peculiar relationship between heat capacities results from a more dramatic equivalence between Bose and Fermi systems. Namely, we prove that the excitations of such Bose and Fermi systems are spectrally equivalent. Two complementary proofs of this equivalence are provided; one based on a combinatoric argument, the other from analysis of the underlying dynamical symmetry group.**Article – URL not found** - E.J. Friedman and A.S. Landsberg. (2001). Large-Scale Synchrony in Weakly Interacting Automata.
*Physical Review E***63:**051303.

Abstract – We study the behavior of two spatially distributed (sandpile) models which are weakly linked with one another. Using a Monte Carlo implementation of the renormalization-group and algebraic methods, we describe how large-scale correlations emerge between the two systems, leading to synchronized behavior.**Article – URL not found** - A. Roomets* and A.S. Landsberg. (2001). Neutral Stability in Josephson Junction Arrays with Arbitrary Lattice Geometry.
*Physics Letters A***283(5-6):**355-359.**Abstract**– We consider DC-biased arrays of overdamped Josephson junctions with different lattice geometries, and demonstrate that, with suitable choice of bias currents, it is possible for the in-phase state of the array to exhibit so-called “neutral stability”. This extends the finding of Wiesenfeld et al. (J. Appl. Phys. 76 (1994) 3835) for two-dimensional rectangular lattices to arbitrary lattice types. - A.S. Landsberg. (2000). Disorder-induced Desynchronization in a 2×2 Circular Josephson Junction Array.
*Physical Review B***61(5):**3641-3648.**Abstract**– Analytical results are presented which characterize the behavior of a dc-biased, two-dimensional circular array of overdamped Josephson junctions subject to increasing levels of disorder. It is shown that high levels of disorder can abruptly destroy the synchronous functioning of the array. We identify the transition boundary between synchronized and desynchronized behavior, along with the mechanism responsible for the loss of frequency locking. Comparisons with recent results for arrays with rectangular lattice geometries are described.

Article - E. Knobloch, A.S. Landsberg, and J. Moehlis. (1999). Chaotic Direction-Reversing Waves.
*Physics Letters A***255(4-6):**287-293.**Abstract**– Symmetry-increasing bifurcations of strange attractors in systems with O(2) symmetry are shown to produce traveling waves that reverse their direction of propagation in a chaotic fashion. The resulting dynamics are illustrated using the normal form describing the triple zero instability.**Article – URL not found** - K. Wiesenfeld, A.S. Landsberg, and G. Fillatrella. (1997). Linewidth Calculation for Bare 2-D Josephson Junction Arrays with Disorder.
*Physics Letters A***233:**373.**Abstract**– We study how disorder affects the frequency-locking properties of a bare current-biased rectangular array of Josephson junctions. Our calculation is based on a simple physical picture wherein elements within each row lock by virtue of spontaneously induced shunt currents through the transverse junctions; no locking occurs between rows. Our analytic formula for the linewidth is in excellent agreement with numerical simulations of the nonlinear circuit equations.**Article – URL not found** - E. Knobloch and A.S. Landsberg. (1996). A New Model of the Solar Cycle.
*Monthly Notices of the Royal Astronomical Society***278:**294. - E.J. Friedman and A.S. Landsberg. (1996). Long Run Dynamics of Queues: Stability and Chaos.
*Operations Research Letters***18(4):**185.

Abstract – We analyze the long-run dynamics of queues in which customers undergo self-selection. We describe the structure and local stability of equilibria for various capacity adjustment procedures and solve the problem of global stability for the limiting cases. The intermediate cases can be quite complicated. We show that one such case leads to chaotic dynamics. - A.S. Landsberg and E.J. Friedman. (1996). Dynamical Effects of Partial Orderings in Physical Systems.
*Physical Review E***54(4):**3135.**Abstract**– We demonstrate that many physical systems possess an often overlooked property known as a partial-ordering structure. The detection and analysis of this special geometric property can be crucial for understanding a system’s dynamical behavior. We review here the fundamental dynamical features common to all such systems, and describe how the partial ordering imposes interesting restrictions on their possible behavior. We show, for instance, that though such systems are capable of displaying highly complex and even chaotic behaviors, most of their experimentally observable behaviors will be simple. Partial orderings are illustrated with examples drawn from many branches of physics, including solid state physics, fluids, and chemical systems. We also describe the consequences of partial orderings on some simple nonlinear models, and prove, for example, that for general two-dimensional mappings with the partial-ordering property, period 3 implies chaos, in analogy with the well-known result of Li and York [Am. Math. Mon. 82, 985 (1975)] for (ordinary) one-dimensional mappings.

Article - A.S. Landsberg and E. Knobloch. (1996). Oscillatory Bifurcation with Broken Translation Symmetry.
*Physical Review E***53(4):**3579.**Abstract**– The effect of distant endwalls on the bifurcation to traveling waves is considered. Previous approaches have treated the problem by assuming that it is a weak perturbation of the translation invariant problem. When the problem is formulated instead in a finite box of length L and the limit L–> [infinity] is taken, one obtains amplitude equations that differ from the usual Ginzburg-Landau description by the presence of an additional nonlinear term. This formulation leads to a description in terms of the amplitudes of the primary box modes, which are odd and even parity standing waves. For large L, the equations that result take the form of a Hopf bifurcation with approximate D4 symmetry. These equations are able to describe, qualitatively, not only traveling and “blinking” states, but also asymmetrical blinking states and “repeated transients,” all of which have been observed in binary fluid convection experiments.

Article - A.S. Landsberg and E. Knobloch. (1996). Oscillatory Doubly Diffusive Convection in a Finite Container.
*Physical Review E***53:**3601.**Abstract**– Oscillatory doubly diffusive convection in a large aspect ratio Hele-Shaw cell is considered. The partial differential equations are reduced via center-unstable manifold reduction to the normal form equations describing the interaction of even and odd parity standing waves near onset. These equations take the form of the equations for a Hopf bifurcation with approximate D4 symmetry, verifying the conclusions of the preceding paper [A.S. Landsberg and E. Knobloch, Phys. Rev. E 53, 3579 (1996)]. In particular, the amplitude equations differ in the limit of large aspect ratios from the usual Ginzburg-Landau description in having additional nonlinear terms with O(1) coefficients. Numerical simulations of the amplitude equations for experimental parameter values are presented and compared with the results of recent experiments by Predtechensky et al. [ Phys. Rev. Lett. 72, 218 (1994); Phys. Fluids 6, 3923 (1994)].

Article - A.S. Landsberg, Y.Braiman, and K. Wiesenfeld. (1995). Disorder and Synchronization in a Josephson Junction Plaquette.
*Applied Physics Letters***67(13):**1935.**Abstract**– We describe the effects of disorder on the coherence properties of a 2 × 2 array of Josephson junctions (a “plaquette”). The disorder is introduced through variations in the junction characteristics. We show that the array will remain one-to-one frequency locked despite large amounts of the disorder, and determine analytically the maximum disorder that can be tolerated before a transition to a desynchronized state occurs. Connections with larger N × M arrays are also drawn.**Article – URL not found** - A.S. Landsberg, Y. Braiman, and K. Wiesenfeld. (1995). Effect of Disorder on Synchronization in Prototype 2-D Josephson Arrays.
*Physical Review B***52(21):**15458.**Abstract**– We study the effects of quenched disorder on the dynamics of two-dimensional arrays of overdamped Josephson junctions. Disorder in both the junction critical currents and resistances is considered. Analytical results for small arrays are used to identify a physical mechanism which promotes frequency locking across each row of the array, and to show that no such locking mechanism exists between rows. The intrarow locking mechanism is surprisingly strong, so that a row can tolerate large amounts of disorder before frequency locking is destroyed.

Article - *A.S. Landsberg. (1993). Spatial Symmetries and Geometrical Phases in Classical Dissipative Systems.
*Modern Physics Letters B***7(2):**71. *(invited article). - E.J. Friedman and A.S. Landsberg. (1993). Short Run Dynamics of Multi-Class Queues.
*Operations Research Letters***14:**221.**Abstract**– We study the dynamics of general queueing systems with multiple classes of customers undergoing self-selection. We prove that if the capacity of a queue is sufficiently large, the equilibrium arrival rate will be globally stable. As the capacity is decreased, the arrival rate typically oscillates near the equilibrium. - A.S. Landsberg and E. Knobloch. (1993). New Types of Waves in Systems with O(2) Symmetry.
*Physics Letters A***179:**316.**Abstract**– A number of novel phenomena arising in systems with O(2) symmetry are described. These include pulsing traveling waves with either a periodically or quasiperiodically modulated phase velocity, and heteroclinic waves which alter their appearance with time, taking successively the form of pure traveling waves, standing waves and steady states. Chaotic waves can also be present. These states result from the codimension-two interaction between a reflection-breaking steady state bifurcation and a reflection-preserving Hopf bifurcation from a circle of nontrivial equilibria. The resulting waveforms are illustrated using a model of magnetoconvection with periodic boundary conditions. - A.S. Landsberg. (1992). Geometrical Phases and Symmetries in Dissipative Systems.
*Physical Review Letters***69(6):**865.**Abstract**– A geometrical phase is constructed for dissipative dynamical systems possessing continuous symmetries. It emerges as the natural analog of the holonomy associated with the adiabatic variation of parameters in quantum-mechanical and classical Hamiltonian systems. In continuous media, the physical manifestation of this phase is a spatial shift of a wave pattern, typically a translation or rotation. An illustration associated with pattern formation in fluids is provided.

Article - A.S. Landsberg and E. Knobloch. (1991). Direction-Reversing Traveling Waves.
*Physics Letters A***159:**17.**Abstract**– A simple mechanism for generating traveling waves which reverse their direction of propagation in a periodic manner is presented. This mechanism is generic in systems possessing O(2) symmetry, and corresponds to a codimension-one symmetry-breaking Hopf bifurcation from a circle of nontrivial steady states.