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We present a theoretical study of a periodic vibrating string composed of a finite sequence of string segments connected periodically, with each segment characterized by a constant linear mass density. The main purpose is to provide a model that can mimic the properties of photonic or phononic crystals. This system displays frequency intervals for which wave propagation is not allowed (frequency bandgaps), in close analogy to photonic and phononic crystals. We discuss the behavior of these bandgaps when varying physical parameters, such as the values of the linear mass densities, the oscillation frequency, and the number of string segments constituting the entire system. [ABSTRACT FROM AUTHOR]

The LIGO analogy lab [Am. J. Phys. 87, 44 (2019)] includes a complicated pair of circuits to sense and control the length of an optical cavity. This Note describes an alternate, Arduino-based controller that is significantly less complex and easier to troubleshoot. The LIGO analogy lab [Am. J. Phys. 87, 44 (2019)] includes advanced experiments in which op-amp-based mixing and feedback circuits are used to lock the length of an optical cavity using heterodyne detection. This Note describes an alternate, Arduino-based controller that implements the heterodyning technique in a significantly less complex and easier to troubleshoot manner. This simplified approach makes the advanced LIGO analog experiments accessible to a wider audience in advanced instructional and optics laboratory courses. [ABSTRACT FROM AUTHOR]

Reasoning by analogy is powerful in physics for students and researchers alike, a case in point being electronics and hydraulics as analogous studies of electric currents and fluid flows. Around 100 years ago, Nikola Tesla proposed a flow control device intended to operate similarly to an electronic diode, allowing fluid to pass easily in one direction but providing high resistance in reverse. Here, we use experimental tests of Tesla's diode to illustrate principles of the electronic-hydraulic analogy. We design and construct a differential pressure chamber (akin to a battery) that is used to measure flow rate (current) and thus resistance of a given pipe or channel (circuit element). Our results prove the validity of Tesla's device, whose anisotropic resistance derives from its asymmetric internal geometry interacting with high-inertia flows, as quantified by the Reynolds number (here, Re ∼ 10 3 ). Through the design and testing of new fluidic diodes, we explore the limitations of the analogy and the challenges of shape optimization in fluid mechanics. We also provide materials that may be incorporated into lesson plans for fluid dynamics courses, laboratory modules, and further research projects. [ABSTRACT FROM AUTHOR]

Raised menisci around small discs positioned to pull up a water-air interface provide a highly controllable experimental setup capable of reproducing much of the rich phenomenology of gravitational lensing (or microlensing) by n-body clusters. Results are shown for single, binary, and triple mass systems. The scheme represents a versatile testbench for the (astro)physics of general relativity's gravitational lens effects, including high multiplicity imaging of extended sources. [ABSTRACT FROM AUTHOR]

Relaxing gap capacitor models emphasize the charge-induced variation of the effective gap of electric double layer capacitors. The first such model, the elastic capacitor, resolved the theoretical puzzle of negative differential capacitance by linking its origin to the charge-induced contraction of the effective gap. It also revealed the importance of treating the electrode charge density as a self-adjustable equilibrium quantity rather than as an independently fixed variable. We show that negative differential capacitance for fixed electrode charge density leads to a charging instability for fixed applied voltage. The "squishy capacitor" model, which allows for lateral variation of the effective gap, relates negative differential capacitance to instabilities' in isolated systems, with a resultant lateral redistribution of surface charge. We review the origin of negative differential capacitance, discuss charging instabilities, and explore the analogy between the critical behavior of the squishy capacitor and first-order phase transitions. [ABSTRACT FROM AUTHOR]

The kinematics of a sphere of radius R and mass m bouncing elastically in a horizontal channel is studied in detail. Explicit expressions for the position and linear and angular velocities of the sphere at any collision are obtained. It is shown that if the moment of inertia 1= γmR2 is such that (1- γ)/(1 + γ)=cos 2π/k with k an integer and k⩾4, the motion is periodic, with repetition after k collisions for k even, and after 2k collisions for k odd. The motion of a homogeneous sphere (which is not periodic) is analyzed by investigating the mean properties of its velocities and positions. The analogy between this motion and that of a periodic oscillator is discussed. [ABSTRACT FROM AUTHOR]