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Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange-Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange-Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange-Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67-98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529-562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014). [ABSTRACT FROM AUTHOR]

For several decades, androgen suppression has been the principal modality for treatment of advanced prostate cancer. Although the androgen deprivation is initially effective, most patients experience a relapse within several years due to the proliferation of so-called androgen-independent tumor cells. Bruchovsky et al. suggested in animal models that intermittent androgen suppression (IAS) can prolong the time to relapse when compared with continuous androgen suppression (CAS). Therefore, IAS has been expected to enhance clinical efficacy in conjunction with reduction in adverse effects and improvement in quality of life of patients during off-treatment periods. This paper presents a mathematical model that describes the growth of a prostate tumor under IAS therapy based on monitoring of the serum prostate-specific antigen (PSA). By treating the cancer tumor as a mixed assembly of androgen-dependent and androgen-independent cells, we investigate the difference between CAS and IAS with respect to factors affecting an androgen-independent relapse. Numerical and bifurcation analyses show how the tumor growth and the relapse time are influenced by the net growth rate of the androgen-independent cells, a protocol of the IAS therapy, and the mutation rate from androgen-dependent cells to androgen-independent ones. [ABSTRACT FROM AUTHOR]

We examine the spatial dynamics of individuals in small schools of banded killifish ( Fundulus diaphanus) that exhibit rhythmic, oscillating speed, typically with sustained, coordinated, out-of-phase speed oscillations as they move around a shallow water tank. We show that the relative motion among the fish yields a periodically time-varying network of social interactions that enriches visually driven social communication. The oscillations lead to the regular making and breaking of occlusions, which we term 'switching.' We show that the rate of convergence to consensus (biologically, the capacity for individuals in groups to achieve effective coordinated motion) governed by the switching outperforms static alternatives, and performs as well as the less practical case of every fish sensing every other fish. We show further that the oscillations in speed yield oscillations in relative bearing between fish over a range that includes the angles previously predicted to be optimal for a fish to detect changes in heading and speed of its neighbors. To investigate systematically, we derive and analyze a dynamic model of interacting agents that move with oscillatory speed. We show that coordinated circular motion of the school leads to systematic cycling of spatial ordering of agents and possibilities for enriched spatial density of measurements of the external environment. Our results highlight the potential benefits of dynamic communication topologies in collective animal behavior, and suggest new, useful control laws for the distributed coordination of mobile robotic networks. [ABSTRACT FROM AUTHOR]

We propose a general framework for the parameter-free identification of a class of dynamical systems. Here, the propagator is approximated in terms of an arbitrary function of the state, in contrast to a polynomial or Galerkin expansion used in traditional approaches. The proposed formulation relies on variational data assimilation using measurement data combined with assumptions on the smoothness of the propagator. This approach is illustrated using a generalized dynamic model describing oscillatory transients from an unstable fixed point to a stable limit cycle and arising in nonlinear stability analysis as an example. This 3-state model comprises an evolution equation for the dominant oscillation and an algebraic manifold for the low- and high-frequency components in an autonomous descriptor system. The proposed optimal model identification technique employs mode amplitudes of the transient vortex shedding in a cylinder wake flow as example measurements. The reconstruction obtained with our technique features distinct and systematic improvements over the well-known mean-field (Landau) model of the Hopf bifurcation. The computational aspect of the identification method is thoroughly validated showing that good reconstructions can also be obtained in the absence of accurate initial approximations. [ABSTRACT FROM AUTHOR]

Dielectrophoresis (DEP) is an electrokinetics-based phenomenon that involves the motion of a particle due to the interaction between an applied nonuniform electric field and an induced dipole moment. This technique is very effective in particle manipulation and separation. Earlier studies on control-amenable models to describe the motion of a neutrally buoyant, neutrally charged particle in a chamber with a parallel electrode array have restricted the motion of the particle to one dimension. Here, incorporating the electro-thermal fluid motion as well, we present a 2D-planar DEP model and study the effect of electro-thermal fluid motion on particle trapping. [ABSTRACT FROM AUTHOR]