We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by re-deriving the Lifshitz formula for infinite half spaces, by demonstrating the Casimir-Polder to van der Waals cross-over, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.

Throughout cell cycle progression, the expression of multiple transcripts oscillate, and whether these are under the centralized control of the CDK-APC/C proteins or can be driven by a de-centralized transcription factor (TF) cascade is a fundamental question for understanding cell cycle regulation. In budding yeast, we find that the transcription of nearly all genes, as assessed by RNA-seq or fluorescence microscopy in single cells, is dictated by CDK-APC/C. Three exceptional genes are transcribed in a pulsatile pattern in a variety of CDK-APC/C arrests. Pursuing one of these transcripts, the SIC1 inhibitor of B-type cyclins, we use a combination of mathematical modeling and experimentation to provide evidence that, counter-intuitively, Sic1 provides a failsafe mechanism promoting nuclear division when levels of mitotic cyclins are low.

We examine whether fluctuation-induced forces can lead to stable levitation. First, we analyze a collection of classical objects at finite temperature that contain fixed and mobile charges, and show that any arrangement in space is unstable to small perturbations in position. This extends Earnshaw's theorem for electrostatics by including thermal fluctuations of internal charges. Quantum fluctuations of the electromagnetic field are responsible for Casimir/van der Waals interactions. Neglecting permeabilities, we find that any equilibrium position of items subject to such forces is also unstable if the permittivities of all objects are higher or lower than that of the enveloping medium; the former being the generic case for ordinary materials in vacuum.Earnshaw's theorem [1] states that a collection of charges cannot be held in stable equilibrium solely by electrostatic forces. The charges can attract or repel, but cannot be stably levitated. While the stability of matter (due to quantum phenomena), and dramatic demonstrations of levitating frogs [2], are vivid reminders of the caveats to this theorem, it remains a powerful indicator of the constraints to stability in electrostatics. There is much current interest in forces induced by fluctuating charges (e.g., mobile ions in solution), or fluctuating electromagnetic (EM) fields (e.g., the Casimir force between metal plates). The former (due to thermal fluctuations) may lead to unexpected phenomena such as attraction of like-charged macroions, and is thought to be relevant to interactions of biological molecules. The latter (due mainly to quantum fluctuations) is important to the attraction (and stiction) of components of microelectromechanical (MEM) devices. Here, we extend Earnshaw's theorem to some fluctuation-induced forces, thus placing strong constraints on the possibility of obtaining stable equilibria, and repulsion between neutral objects.An extension of Earnshaw's theorem [1] to polarizable objects by Braunbek [3,4] establishes that dielectric and paramagnetic ( > 1 and µ > 1) matter cannot be stably levitated by electrostatic forces, while diamagnetic (µ < 1) matter can. This is impressively demonstrated by superconductors and frogs that fly freely above magnets [2]. If the enveloping medium is not vacuum, the criteria for stability are modified by substituting the static electric permittivity M and magnetic permeability µ M of the medium in place of the vacuum value of 1 in the respective inequalities. In fact, if the medium itself has a dielectric constant higher than the objects ( < M ), stable levitation is possible, as demonstrated for bubbles in liquids (see Ref. [5], and references therein). For dynamic fields the restrictions of electrostatics do not apply; for example, lasers can lift and hold dielectric beads with index of refraction n = √ µ > 1 [6]. In addition to the force which keeps the bead in the center of the laser beam, there is radiation pressure which pushes the bead along the direction of the Poynting vector. Ashkin and Gordon hav...

We study collective interaction effects that result from the change of free quantum electrodynamic field fluctuations by one-and two-dimensional perfect metal structures. The Casimir interactions in geometries containing plates and cylinders is explicitly computed using partial wave expansions of constrained path integrals. We generalize previously obtained results and provide a more detailed description of the technical aspects of the approach [1]. We find that the interactions involving cylinders have a weak logarithmic dependence on the cylinder radius, reflecting that one-dimensional perturbations are marginally relevant in 4D space-time. For geometries containing two cylinders and one or two plates, we confirm a previously found non-monotonic dependence of the interaction on the object's separations which does not follow from pair-wise summation of two-body forces. Qualitatively, this effect is explained in terms of fluctuating charges and currents and their mirror images.