Dynamics of bacterial flow: Emergence of spatiotemporal coherent structures (2007)
Sambelashvili, Nicholas, Lau, A. W. C., Cai, David
We propose a simple model of self-propelled particles to show that coherent structures, such as jets and swirls, can arise from a plausible microscopic mechanisms: (i) the elongated shape of the...
Interactions of renormalized waves in thermalized Fermi-Pasta-Ulam chains (2007)
Gershgorin, Boris, Lvov, Yuri V., Cai, David
The dispersive interacting waves in Fermi-Pasta-Ulam (FPU) chains of particles in \textit{thermal equilibrium} are studied from both statistical and wave resonance perspectives. It is shown that,...
Kinetic theory for neuronal network dynamics (2006)
Cai, David, Tao, Louis, Rangan, Aaditya V., McLaughlin, David W.
We present a detailed theoretical framework for statistical descriptions of neuronal networks and derive $(1+1)$-dimensional kinetic equations, without introducing any new parameters, directly from...
Renormalized waves and discrete breathers in $\beta$-FPU chains (2005)
Gershgorin, Boris, Lvov, Yuri V., Cai, David
We demonstrate via numerical simulation that in the \textit{strongly} nonlinear limit, the $\beta$-FPU system in thermal equilibrium behaves surprisingly like weakly nonlinear waves in properly...
A Mathematical Framework for Quantifying Predictability Through Relative Entropy (2002)
Cai, David, Kleeman, Richard, Majda, Andrew
Kleeman has recently demonstrated that the relative entropy provides a significant measure of the information content of a prediction ensemble compared with the climate record in several simplified...
The nonlinear Schrödinger equation as both a PDE and a dynamical system (2002)
A Dynamical System, David Cai, David W. Mclaughlin
Nonlinear dispersive wave equations provide excellent examples of innite dimensional dynamical systems which possess diverse and fascinating phenomena including solitary waves and wave trains, the...
Cai, David, Gronbech-Jensen, Niels, Snell, Charles M., Beardmore, Keith M.
It is crucial to have a good phenomenological model of electronic stopping power for modeling the physics of ion implantation into crystalline silicon. In the spirit of the Brandt-Kitagawa effective...
Localized States in Discrete Nonlinear Schr\"{o}dinger Equations (1993)
Cai, David, Bishop, A. R., Grønbech-Jensen, Niels
A new 1-D discrete nonlinear Schr\"{o}dinger (NLS) Hamiltonian is introduced which includes the integrable Ablowitz-Ladik system as a limit. The symmetry properties of the system are studied. The...
Length-scale competition in the damped sine-Gordon chain (1992)
Cai, David, Bishop, A. R., Sanchez, Angel
It is shown that there are two different regimes for the damped sine-Gordon chain driven by the spatio-temporal periodic force $\Gamma sin(\omega t - k_{n} x)$ with a flat initial condition. For...
Spectral bifurcations in dispersive wave turbulence
Cai, David, Majda, Andrew J., McLaughlin, David W., Tabak, Esteban G.
Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct...
Cai, David, Tao, Louis, Shelley, Michael, McLaughlin, David W.
A coarse-grained representation of neuronal network dynamics is developed in terms of kinetic equations, which are derived by a moment closure, directly from the original large-scale...
Cai, David, Tao, Louis, McLaughlin, David W.
To address computational “scale-up” issues in modeling large regions of the cortex, many coarse-graining procedures have been invoked to obtain effective descriptions of neuronal network...
Architectural and synaptic mechanisms underlying coherent spontaneous activity in V1
Cai, David, Rangan, Aaditya V., McLaughlin, David W.
To investigate the existence and the characteristics of possible cortical operating points of the primary visual cortex, as manifested by the coherent spontaneous ongoing activity revealed by...
Rangan, Aaditya V., Cai, David, McLaughlin, David W.
Our large-scale computational model of the primary visual cortex that incorporates orientation-specific, long-range couplings with slow NMDA conductances operates in a fluctuating dynamic state of...
Spectral bifurcations in dispersive wave turbulence
Cai, David, Majda, Andrew J., McLaughlin, David W., Tabak, Esteban G.
Dispersive wave turbulence is studied numerically for a class of one-dimensional nonlinear wave equations. Both deterministic and random (white noise in time) forcings are studied. Four distinct...
Cai, David, Tao, Louis, Shelley, Michael, McLaughlin, David W.
A coarse-grained representation of neuronal network dynamics is developed in terms of kinetic equations, which are derived by a moment closure, directly from the original large-scale...
Cai, David, Tao, Louis, McLaughlin, David W.
To address computational “scale-up” issues in modeling large regions of the cortex, many coarse-graining procedures have been invoked to obtain effective descriptions of neuronal network...
Architectural and synaptic mechanisms underlying coherent spontaneous activity in V1
Cai, David, Rangan, Aaditya V., McLaughlin, David W.
To investigate the existence and the characteristics of possible cortical operating points of the primary visual cortex, as manifested by the coherent spontaneous ongoing activity revealed by...
Rangan, Aaditya V., Cai, David, McLaughlin, David W.
Our large-scale computational model of the primary visual cortex that incorporates orientation-specific, long-range couplings with slow NMDA conductances operates in a fluctuating dynamic state of...
Orientation selectivity in visual cortex by fluctuation-controlled criticality
Tao, Louis, Cai, David, McLaughlin, David W., Shelley, Michael J., Shapley, Robert
Within a large-scale neuronal network model of macaque primary visual cortex, we examined how intrinsic dynamic fluctuations in synaptic currents modify the effect of strong recurrent excitation on...
Quantifying neuronal network dynamics through coarse-grained event trees
Rangan, Aaditya V., Cai, David, McLaughlin, David W.
Animals process information about many stimulus features simultaneously, swiftly (in a few 100 ms), and robustly (even when individual neurons do not themselves respond reliably). When the brain...