Casimir forces in the time domain II: Applications

Our preceding paper introduced a method to compute Casimir forces in arbitrary geometries and for arbitrary materials that was based on a finite-difference time-domain (FDTD) scheme. In this manuscript, we focus on the efficient implementation of our method for geometries of practical interest and extend our previous proof-of-concept algorithm in one dimension to problems in two and three dimensions, introducing a number of new optimizations. We consider Casimir piston-like problems with nonmonotonic and monotonic force dependence on sidewall separation, both for previously solved geometries to validate our method and also for new geometries involving magnetic sidewalls and/or cylindrical pistons. We include realistic dielectric materials to calculate the force between suspended silicon waveguides or on a suspended membrane with periodic grooves, also demonstrating the application of PML absorbing boundaries and/or periodic boundaries. In addition we apply this method to a realizable three-dimensional system in which a silica sphere is stably suspended in a fluid above an indented metallic substrate. More generally, the method allows off-the-shelf FDTD software, already supporting a wide variety of materials (including dielectric, magnetic, and even anisotropic materials) and boundary conditions, to be exploited for the Casimir problem.Comment: 11 pages, 12 figures. Includes additional examples (dispersive materials and fully three-dimensional systems

Casimir repulsion between metallic objects in vacuum

We give an example of a geometry in which two metallic objects in vacuum experience a repulsive Casimir force. The geometry consists of an elongated metal particle centered above a metal plate with a hole. We prove that this geometry has a repulsive regime using a symmetry argument and confirm it with numerical calculations for both perfect and realistic metals. The system does not support stable levitation, as the particle is unstable to displacements away from the symmetry axis.Comment: 4 pages, 4 figures; added references, replaced Fig.

Achieving a Strongly Temperature-Dependent Casimir Effect

We propose a method of achieving large temperature sensitivity in the Casimir force that involves measuring the stable separation between dielectric objects immersed in fluid. We study the Casimir force between slabs and spheres using realistic material models, and find large > 2nm/K variations in their stable separations (hundreds of nanometers) near room temperature. In addition, we analyze the effects of Brownian motion on suspended objects, and show that the average separation is also sensitive to changes in temperature . Finally, this approach also leads to rich qualitative phenomena, such as irreversible transitions, from suspension to stiction, as the temperature is varied

Will Changing Demographics Affect U.S. Cheese Demand?

U.S. cheese consumption has grown considerably over the last three decades. Using a censored demand model and Nielsen Homescan retail data, this study identifies price and non-price factors affecting the demand for differentiated cheese products. Own-price and expenditure elasticities for all of the cheese products are statistically significant and elastic. Results also reveal that a strong substitution relationship exists among all cheese products. Although demographic influences are generally smaller than those related to prices and expenditures, empirical findings show that household size, college educated female heads of household who are age 40 and older, residing in the South, Central, and Western regions of the United States, as well as Black heads of household, have positive statistically significant effects on consumers’ cheese purchases.cheese form, cheese purchase, demand elasticities, demographic and economic factors, Nielsen Homescan data, Food Consumption/Nutrition/Food Safety, Marketing, C25, D12, Q11,

Structural anisotropy and orientation-induced Casimir repulsion in fluids

In this work we theoretically consider the Casimir force between two periodic arrays of nanowires (both in vacuum, and on a substrate separated by a fluid) at separations comparable to the period. Specifically, we compute the dependence of the exact Casimir force between the arrays under both lateral translations and rotations. Although typically the force between such structures is well-characterized by the Proximity Force Approximation (PFA), we find that in the present case the microstructure modulates the force in a way qualitatively inconsistent with PFA. We find instead that effective-medium theory, in which the slabs are treated as homogeneous, anisotropic dielectrics, gives a surprisingly accurate picture of the force, down to separations of half the period. This includes a situation for identical, fluid-separated slabs in which the exact force changes sign with the orientation of the wire arrays, whereas PFA predicts attraction. We discuss the possibility of detecting these effects in experiments, concluding that this effect is strong enough to make detection possible in the near future.Comment: 12 pages, 9, figure. Published version with expanded discussio

Designing evanescent optical interactions to control the expression of Casimir forces in optomechanical structures

We propose an optomechanical structure consisting of a photonic-crystal (holey) membrane suspended above a layered silicon-on-insulator substrate in which resonant bonding/antibonding optical forces created by externally incident light from above enable all-optical control and actuation of stiction effects induced by the Casimir force. In this way, one can control how the Casimir force is expressed in the mechanical dynamics of the membrane, not by changing the Casimir force directly but by optically modifying the geometry and counteracting the mechanical spring constant to bring the system in or out of regimes where Casimir physics dominate. The same optical response (reflection spectrum) of the membrane to the incident light can be exploited to accurately measure the effects of the Casimir force on the equilibrium separation of the membrane