Nonlinear Dynamics of Particles Excited by an Electric Curtain

The use of the electric curtain (EC) has been proposed for manipulation and control of particles in various applications. The EC studied in this paper is called the 2-phase EC, which consists of a series of long parallel electrodes embedded in a thin dielectric surface. The EC is driven by an oscillating electric potential of a sinusoidal form where the phase difference of the electric potential between neighboring electrodes is 180 degrees. We investigate the one- and two-dimensional nonlinear dynamics of a particle in an EC field. The form of the dimensionless equations of motion is codimension two, where the dimensionless control parameters are the interaction amplitude ($A$) and damping coefficient ($\beta$). Our focus on the one-dimensional EC is primarily on a case of fixed $\beta$ and relatively small $A$, which is characteristic of typical experimental conditions. We study the nonlinear behaviors of the one-dimensional EC through the analysis of bifurcations of fixed points. We analyze these bifurcations by using Floquet theory to determine the stability of the limit cycles associated with the fixed points in the Poincar\'e sections. Some of the bifurcations lead to chaotic trajectories where we then determine the strength of chaos in phase space by calculating the largest Lyapunov exponent. In the study of the two-dimensional EC we independently look at bifurcation diagrams of variations in $A$ with fixed $\beta$ and variations in $\beta$ with fixed $A$. Under certain values of $\beta$ and $A$, we find that no stable trajectories above the surface exists; such chaotic trajectories are described by a chaotic attractor, for which the the largest Lyapunov exponent is found. We show the well-known stable oscillations between two electrodes come into existence for variations in $A$ and the transitions between several distinct regimes of stable motion for variations in $\beta$

Mathematical analysis of a model for the growth of the bovine corpus luteum

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2).\ud \ud In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system.\ud \ud We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, p5. We find that weak (low p5) or strong (high p5) angiogenesis leads to ‘pathological’ CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of p5, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows

Long-range interacting pendula: A simple model for understanding complex dynamics of charged particles in an electronic curtain device

In this paper, we investigate the equilibrium and non-equilibrium properties of a model that shares several important characteristics with charged particles interacting in an Electric Curtain (EC) device. An EC comprises a periodic array of parallel electrodes, applied to each is an alternating electric potential. Depending on the applied potentials and the geometry of the electrodes, a wide variety of field structures above the plane of the electrodes are possible. The EC has multiple applications in the control and manipulation of small particles, but is under utilized in industry and science because of difficulties in predicting and understanding the particle dynamics. One particular challenge in understanding the dynamics is the many-body coulomb interactions. To better understand the role of the interactions, we study a one-dimensional analytically tractable model that encapsulates their long-range nature. Specifically, we study a Hamiltonian similar to that of the Hamiltonian mean field model but with the inclusion of an index dependent phase in the interaction term that, as we show, reflects the periodic structure of an EC field. We solve for the canonical partition function and also investigate some of the non-equilibrium behaviors. In the study of the non-equilibrium behaviors, we find an interesting property, namely that a quasistationary (lifetime diverges as the number of particles is increased) clustered state can exist when an initial configuration is ordered by the particle indices

Can winter-active bumblebees survive the cold?:Assessing the cold tolerance of Bombus terrestris audax and the effects of pollen feeding

There is now considerable evidence that climate change is disrupting the phenology of key pollinator species. The recently reported UK winter activity of the bumblebee Bombus terrestris brings a novel set of thermal challenges to bumblebee workers that would typically only be exposed to summer conditions. Here we assess the ability of workers to survive acute and chronic cold stress (via lower lethal temperatures and lower lethal times at 0°C), the capacity for rapid cold hardening (RCH) and the influence of diet (pollen versus nectar consumption) on supercooling points (SCP). Comparisons are made with chronic cold stress indices and SCPs in queen bumblebees. Results showed worker bees were able to survive acute temperatures likely to be experienced in a mild winter, with queens significantly more tolerant to chronic cold temperature stress. The first evidence of RCH in any Hymenoptera is shown. In addition, dietary manipulation indicated the consumption of pollen significantly increased SCP temperature. These results are discussed in the light of winter active bumblebees and climate change

Computational studies of multiple-particle nonlinear dynamics in a spatio-temporally periodic potential

The spatio-temporally periodic (STP) potential is interesting in Physics due to the intimate coupling between its time and spatial components. In this paper, we begin with a brief discussion of the dynamical behaviors of a single particle in a STP potential and then examine the dynamics of multiple particles interacting in a STP potential via the electric Coulomb potential. For the multiple particles\u27 case, we focus on the occurrence of bifurcations when the amplitude of the STP potential varies. It is found that the particle concentration of the system plays an important role; the type of bifurcations that occur and the number of attractors present in the Poincaré sections depend on whether the number of particles in the simulation is even or odd. In addition to the nonlinear dynamical approach, we also discuss dependence of the squared fractional deviation of particles\u27 kinetic energy of the multiple particle system on the amplitude of the STP potential which can be used to elucidate certain transitions of states; this approach is simple and useful particularly for experimental studies of complicated interacting systems. © 2014 AIP Publishing LLC

Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime

When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E_{jk} that describes tidal gravity and a "magnetic" part B_{jk} that describes differential dragging of inertial frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines, their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity, and tendexes), and also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.Comment: 4 pages, 5 figure

Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime

When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E_{jk} that describes tidal gravity and a "magnetic" part B_{jk} that describes differential dragging of inertial frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines, their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity, and tendexes), and also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.Comment: 4 pages, 5 figure

Mathematical analysis of a model for the growth of the bovine corpus luteum.

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2). In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system. We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, ρ₅. We find that weak (low ρ₅) or strong (high ρ₅) angiogenesis leads to 'pathological' CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of ρ₅, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows

Trace metal fluxes to the ocean: The importance of high‐standing oceanic islands

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94592/1/grl16149.pd