Minimal resistance of curves under the single impact assumption

We consider the hollow on the half-plane $\{ (x,y) : y \le 0 \} \subset \mathbb{R}^2$ defined by a function $u : (-1,\, 1) \to \mathbb{R}$, $u(x) < 0$, and a vertical flow of point particles incident on the hollow. It is assumed that $u$ satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph$(u)$ and goes away without hitting the graph of $u$ anymore. We solve the problem: find the function $u$ minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the $y$-axis. Assuming that the resistance of $u \equiv 0$ equals 1, we show that the minimal resistance equals $\pi/2 - 2\arctan(1/2) \approx 0.6435$. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730--2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space $\{(x_1,\ldots,x_d, y) : y \le 0 \} \subset \mathbb{R}^{d+1}$ is defined by a radial function $U$ satisfying the SIC, $U(x) = u(|x|)$, with $x = (x_1,\ldots,x_d)$, $u(\xi) < 0$ for $0 \le \xi < 1$, and $u(\xi) = 0$ for $\xi \ge 1$, and the flow is parallel to the $y$-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as $d \to \infty$

Optimal Planar Electric Dipole Antenna

Considerable time is often spent optimizing antennas to meet specific design metrics. Rarely, however, are the resulting antenna designs compared to rigorous physical bounds on those metrics. Here we study the performance of optimized planar meander line antennas with respect to such bounds. Results show that these simple structures meet the lower bound on radiation Q-factor (maximizing single resonance fractional bandwidth), but are far from reaching the associated physical bounds on efficiency. The relative performance of other canonical antenna designs is compared in similar ways, and the quantitative results are connected to intuitions from small antenna design, physical bounds, and matching network design.Comment: 10 pages, 15 figures, 2 tables, 4 boxe

Geometrically asymmetric electrodes for probing electrochemical reaction kinetics: a case study of hydrogen at the Pt–CsH_2PO_4 interface

Electrochemical reactions can exhibit considerable asymmetry, with the polarization behavior of oxidation at a given metal|electrolyte interface differing substantially from that of reduction. The reference-less, microcontact electrode geometry, in which the electrode overpotentials are geometrically constrained to the working electrode (by limiting its area) is experimentally convenient, particularly for fuel cell studies, because the results do not rely on accurate placement of a reference electrode nor must oxidant and reductant gases be sealed off from one another. Here, the conditions under which the critical assumption of this geometry applies -— that the overpotential at the large-area counter electrode can be ignored -— is numerically assessed. It is found that, for cells of sufficiently large area, the effective radius of the counter electrode (which defines the area through which the majority of the current passes) can be expressed directly as a function of electrolyte thickness and the materials properties, σ, the conductivity of the electrolyte, and k, the reaction rate constant for the electrochemical reaction at zero-bias. From this effective radius and the true radius of the working electrode, the fraction of electrode overpotential at the latter, defined as the extent of isolation, can be readily computed. Experimental studies of hydrogen electro-oxidation/proton electro-reduction at the Pt|CsH_2PO_4 interface using two cells of differing dimensions both validate the computational results and demonstrate that asymmetry in such reactions are readily revealed in the micro-electrode, reference-less geometry. The study furthermore confirms the insensitivity of the results to the precise placement of the working electrode, while indicating the importance of very high isolation values (>99%) to ensure that overpotential contributions of the counter electrode do not influence the measurements, particularly as bias is increased

On the two-dimensional rotational body of maximal Newtonian resistance

We investigate, by means of computer simulations, shapes of nonconvex bodies that maximize resistance to their motion through a rarefied medium, considering that bodies are moving forward and at the same time slowly rotating. A two-dimensional geometric shape that confers to the body a resistance very close to the theoretical supremum value is obtained, improving previous results.Comment: This is a preprint version of the paper published in J. Math. Sci. (N. Y.), Vol. 161, no. 6, 2009, 811--819. DOI:10.1007/s10958-009-9602-

A linear nonequilibrium thermodynamics approach to optimization of thermoelectric devices

Improvement of thermoelectric systems in terms of performance and range of applications relies on progress in materials science and optimization of device operation. In this chapter, we focuse on optimization by taking into account the interaction of the system with its environment. For this purpose, we consider the illustrative case of a thermoelectric generator coupled to two temperature baths via heat exchangers characterized by a thermal resistance, and we analyze its working conditions. Our main message is that both electrical and thermal impedance matching conditions must be met for optimal device performance. Our analysis is fundamentally based on linear nonequilibrium thermodynamics using the force-flux formalism. An outlook on mesoscopic systems is also given.Comment: Chapter 14 in "Thermoelectric Nanomaterials", Editors Kunihito Koumoto and Takao Mori, Springer Series in Materials Science Volume 182 (2013

Microwave photovoltage and photoresistance effects in ferromagnetic microstrips

We investigate the dc electric response induced by ferromagnetic resonance in ferromagnetic Permalloy (Ni80Fe20) microstrips. The resulting magnetization precession alters the angle of the magnetization with respect to both dc and rf current. Consequently the time averaged anisotropic magnetoresistance (AMR) changes (photoresistance). At the same time the time-dependent AMR oscillation rectifies a part of the rf current and induces a dc voltage (photovoltage). A phenomenological approach to magnetoresistance is used to describe the distinct characteristics of the photoresistance and photovoltage with a consistent formalism, which is found in excellent agreement with experiments performed on in-plane magnetized ferromagnetic microstrips. Application of the microwave photovoltage effect for rf magnetic field sensing is discussed.Comment: 16 pages, 15 figure