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A general specialization map is constructed for higher Chow groups and used to prove a "going-up" theorem for algebraic cycles and their regulators. The results are applied to study the degeneration of the modified diagonal cycle of Gross…
The intransitive cycle of superiority is characterized by such binary relations between A, B, and C that A is superior to B, B is superior to C, and C is superior to A (i.e., A>B>C>A - in contrast with transitive relations A>B>C). The first…
The Dirac belt trick is often employed in physics classrooms to show that a $2\pi$ rotation is not topologically equivalent to the absence of rotation whereas a $4\pi$ rotation is, mirroring a key property of quaternions and their…
We have developed dualization of ordinary and ``Stueckelberg compensated'' massive phase for the Kalb-Ramond theory. The compensated phase allows to study the interplay between spin jumping and duality. We show that spin jumping is caused…
The role of spin is investigated in the transport through a quantum dot with two overlapping resonances (one having a width larger than the level separation and the other very narrow, cf. Silvestrov and Imry, Phys. Rev. Lett. {\bf 85}, 2565…
Some new developments obtained in the last few years concerning the propagation of high energy cosmic rays are discussed. In particular, it is shown how the inclusion of drift effects in the transport diffusion equations leads naturally to…
In this chapter, we review some of the interesting consequences that tilt between the spin axis of the black hole and angular momentum axis of the accretion disk can have on the dynamics, thermodynamics, and observational appearance of…
One of the central problems in High T_{c} superconductivity is to reconcile the abundant evidence for stripe-like physics at `short' distances with the equally convincing evidence for BCS like physics at large distance scales (the `nodal…
For polyhedral convex cones in ${\mathbb R}^d$, we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic…
A new approach to the local and global explanation is proposed. It is based on selecting a convex hull constructed for the finite number of points around an explained instance. The convex hull allows us to consider a dual representation of…
Bilayers of two-dimensional materials twisted at specific angles can exhibit exceptional properties such as the occurrence of unconventional superconductivity in twisted graphene. We demonstrate here that novel phenomena in twisted…
A beer bottle or soda can on a table, when slightly tipped and released, falls to an upright position and then rocks up to a somewhat opposite tilt. Superficially this rocking motion involves a collision when the flat circular base of the…
In this paper three notions of emergent geometry arising from the study of gauge/gravity duals are discussed. The unifying theme behind these notions of emergent geometry is that one can derive properties of the effective action of a probe…
With the goal of providing more accurate and realistic estimates of the secular behavior of the mass accretion and drag rates in the "common-envelope" scenario encountered when a black hole or a neutron star moves in the stellar envelope of…
In this paper, I outline some problems in the students' understanding of the explanation of recoil motion when introduced to them in the context of Newton's third law. I propose to explain the origin of recoil from a microscopic point of…
The double pendulum, a simple system of classical mechanics, is widely studied as an example of, and testbed for, chaotic dynamics. In 2016, Maiti et al. studied a generalization of the simple double pendulum with equal point-masses at…
Vakonomic mechanics has been proposed as a possible description of the dynamics of systems subject to nonholonomic constraints. The aim of the present work is to show that for an important physical system the motion brought about by…
We present a model system for objects, climbers, which have the ability to move as ASEP particles with non-uniform forward and backward jumping rate dynamics. These climbers are implemented as Mandal-Quan-Jarzynski [1] machines. Climbers on…
This article starts with the mathematical definition, concrete description, and physical meaning of Cartan's torsion. I proceed with the argumentation that torsion is required for the description of intrinsic spin. Moreover I argue that the…
A Radon-type transform called a cone transform that assigns to a given function its integral over various sets of cones has arisen in the last decade in the context of the study of Compton cameras used in Single Photon Emission Computed…