Louis F. Rossi

Resurrecting Core Spreading Vortex Methods: A New Scheme That Is Both Deterministic and Convergent

A basic core spreading vortex scheme is inconsistent but can be corrected with a splitting algorithm, yielding a deterministic and efficient grid-free method for viscous flows. The splitting algorithm controls the consistency error by maintaining small vortex core sizes. Routine analysis will show that the core spreading method coupled to this splitting process is convergent in

Quantifying and Tracing Information Cascades in Swarms

L^p

Quasi-steady monopole and tripole attractors for relaxing vortices

spaces. Analysis of the linearized residual operator establishes the uniform convergence of this method when the exact flow field is known. A sequence of examples demonstrates the sensitivity of the method to numerical parameters as the computed solution converges to the exact solution. These experimental results agree with the linear convergence theory. Finally, direct comparisons between the traditional random walk vortex method and the new method indicate that the new method has several advantages while requiring the same computational effort.

Slime mold inspired routing protocols for wireless sensor networks

We propose a novel, information-theoretic, characterisation of cascades within the spatiotemporal dynamics of swarms, explicitly measuring the extent of collective communications. This is complemented by dynamic tracing of collective memory, as another element of distributed computation, which represents capacity for swarm coherence. The approach deals with both global and local information dynamics, ultimately discovering diverse ways in which an individual’s spatial position is related to its information processing role. It also allows us to contrast cascades that propagate conflicting information with waves of coordinated motion. Most importantly, our simulation experiments provide the first direct information-theoretic evidence (verified in a simulation setting) for the long-held conjecture that the information cascades occur in waves rippling through the swarm. Our experiments also exemplify how features of swarm dynamics, such as cascades’ wavefronts, can be filtered and predicted. We observed that maximal information transfer tends to follow the stage with maximal collective memory, and principles like this may be generalised in wider biological and social contexts.

The evolution of Kirchhoff elliptic vortices

Using fully nonlinear simulations of the two-dimensional Navier–Stokes equations at large Reynolds number (Re), we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing.

Merging Computational Elements in Vortex Simulations

Many biological systems are composed of unreliable components which self-organize effectively into systems that achieve a balance between efficiency and robustness. One such example is the true slime mold Physarum polycephalum which is an amoeba-like organism that seeks and connects food sources and efficiently distributes nutrients throughout its cell body. The distribution of nutrients is accomplished by a self-assembled resource distribution network of small tubes with varying diameter which can evolve with changing environmental conditions without any global control. In this paper, we exploit two different mechanisms of the slime mold’s tubular network formation process via laboratory experiments and mathematical behavior modeling to design two corresponding localized routing protocols for wireless sensor networks (WSNs) that take both efficiency and robustness into account. In the first mechanism of path growth, slime mold explores its immediate surroundings to discover and connect new food sources during its growth cycle. We adapt this mechanism for a path growth routing protocol by treating data sources and sinks as singular potentials to establish routes from the sinks to all the data sources. The second mechanism of path evolution is the temporal evolution of existing tubes through nonlinear feedback in order to distribute nutrients efficiently throughout the organism. Specifically, the diameters of tubes carrying large fluxes of nutrients grow to expand their capacities, and tubes that are not used decline and disappear entirely. We adapt the tube dynamics of the slime mold for a path evolution routing protocol. In our protocol, we identify one key adaptation parameter to adjust the tradeoff between efficiency and robustness of network routes. Through extensive realistic network simulations and ideal closed form or numerical computations, we validate the effectiveness of both protocols, as well as the efficiency and robustness of the resulting network connectivity.

Slime mold inspired path formation protocol for wireless sensor networks

A Kirchhoff elliptic vortex is a two-dimensional elliptical region of uniform vorticity embedded in an inviscid, incompressible, and irrotational fluid. By using analytic theory and contour dynamics simulations, we describe the evolution of perturbed Kirchhoff vortices by decomposing solutions into constituent linear eigenmodes. With small amplitude perturbations, we find excellent agreement between the short time dynamics and the predictions of linear analytic theory. Elliptical vortices must have aspect ratios less than a∕b=3 to be completely stable. At late times, unstable perturbations evolve to states consisting of filaments surrounding and connecting one or more separate vortex core regions. Even modes have two different evolution paths accessible to them, dependent on the initial phase. Ellipses can first fission into more than one separate region when a∕b=6.046, from the negative branch m=4 mode. Increasing the perturbation amplitude can result in nonlinear instability, while the perturbation is s...

A continuum three-zone model for swarms.

This paper analyzes the process of merging groups of many Gaussian basis functions into a single basis function in vortex simulations. Analysis of the equations governing this process yields fundamental parameters and uniform estimates of the merger-induced error. In a merging event, the uniform error bound depends only on relationships between nearby computational elements permitting fast and effective merging schemes. In this paper, one such algorithm is proposed and demonstrated.

Achieving High-Order Convergence Rates with Deforming Basis Functions

Many biological systems are composed of unreliable components which self-organize efficiently into systems that can tackle complex problems. One such example is the true slimemold Physarum polycephalum which is an amoeba-like organism that seeks food sources and efficiently distributes nutrients throughout its cell body. The distribution of nutrients is accomplished by a self-assembled resource distribution network of small tubes with varying diameter which can evolve with changing environmental conditions without any global control. In this paper, we use a phenomenological model for the tube evolution in slime mold and map it to a path formation protocol for wireless sensor networks. By selecting certain evolution parameters in the protocol, the network may evolve toward single paths connecting data sources to a data sink. In other parameter regimes, the protocol may evolve toward multiple redundant paths. We present detailed analysis of a small model network. A thorough understanding of the simple network leads to design insights into appropriate parameter selection. We also validate the design via simulation of large-scale realistic wireless sensor networks using the QualNet network simulator.

Modeling, analysis and simulation of ant-based network routing protocols

We present a progression of three distinct three-zone, continuum models for swarm behavior based on social interactions with neighbors in order to explain simple coherent structures in popular biological models of aggregations. In continuum models, individuals are replaced with density and velocity functions. Individual behavior is modeled with convolutions acting within three interaction zones corresponding to repulsion, orientation, and attraction, respectively. We begin with a variable-speed first-order model in which the velocity depends directly on the interactions. Next, we present a variable-speed second-order model. Finally, we present a constant-speed second-order model that is coordinated with popular individual-based models. For all three models, linear stability analysis shows that the growth or decay of perturbations in an infinite, uniform swarm depends on the strength of attraction relative to repulsion and orientation. We verify that the continuum models predict the behavior of a swarm of individuals by comparing the linear stability results with an individual-based model that uses the same social interaction kernels. In some unstable regimes, we observe that the uniform state will evolve toward a radially symmetric attractor with a variable density. In other unstable regimes, we observe an incoherent swarming state.