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\dot{\theta}_k(t) = \omega + \frac{k}{n} \sum_{i=1}^n \sin\left(\theta_i(t) - \theta_k(t)\right). [[File:Coupled_Oscillators_11.png | thumb | 300px | right | Figure 1: Phases of 11 Coupled Harmonic Oscillators.]]

...particles (~10nm) that react paramagnetically to a uniform magnetic field [1]. The fluid becomes magnetized in the presence of a magnetic field and un- ...nly used in mechanical, medical, aerospace, optical and other applications[1], the dynamic behavior of these fluids appears to be vastly under studied.

...nline&aid=283922 | journal=Journal of Fluid Mechanics | volume=526 | pages=1-17}}</ref>. However, it is not very precise, and gives very little informat ...& Fuchikami<ref name="K&F" /> adopt a set of geometrized units such that g=1. For water at twenty degrees centigrade, these units are l0=0.27 cm, t0=0.0

...the stutter jump (dashed). A transition point occurs at $\alpha \approx 0.1$. Below this value, the stutter jump performs better. {| border="1" class="wikitable"

[[File:built_chua.png|thumb|400px|alt=text|Figure 1: Two Chua Circuits on a single breadboard]] ...plicated the circuit diagram in Figure (1). It has four major components: (1) a variable resistor, whose resistance acts as the control variable, (2) tw

: Eponymously discovered by Faraday[1], Faraday Waves are standing waves on a fluid caused by vertical oscillator ...t \left(\nabla\vec{v} + \nabla\vec{v}^T \right)+ \frac{1}{Fr}F(cos(2\pi t)-1)\mathbf{j}</math>

1. What amplitudes and frequencies of periodic forcing allow the inverted pen <math>\frac{\delta v}{\delta t}=-\frac{v}{Q \Omega}-\left[\frac{1}{\Omega^{2}}-\epsilon*cn(t,m)\right]*\sin{\theta}</math>

...d the aggregate statistics of the outcomes based on the starting position [1,2]. These analyses assume that each puck-pin interaction can only result i ...t on the puck velocity. The acceleration from the magnets is modeled as a 1/r^2 function, which should be valid for small magnets spaced far apart. Th

Where $x_i$ is the state of an oscillator with $x_i \in [0,1]$, $S_0$ is a property of the x_i = 1 \Rightarrow \; x_j(t^+) = \eta + x_j(t) \quad \forall j \neq i

...tup is shown to the right, with the metronomes always being placed along a 1-dimensional array. \ddot\phi_j+b\dot\phi_j+\frac{g}{l}\sin\phi_j=-\frac{1}{l}\ddot X \cos\phi_j+F_j

\scriptsize{L = \frac{1}{2}\dot{q}^TM\dot{q}-V(q)} Figures 1 thru 3 demonstrate that the active time of the end bobs increased as the As