Related papers: Qi-Wa, a problem that has plagued Chinese scrolls …
The recently discovered alignment of quasar polarizations on very large scales could possibly explained by considering cosmic strings on a warped five dimensional spacetime. Compact objects, such as cosmic strings, could have tremendous…
When studying the history of mathematical symbols, one finds that the development of mathematical symbols in China is a significant piece of Chinese history; however, between the beginning of mathematics and modern day mathematics in China,…
Two-dimensional (2D) materials can roll up, forming stable scrolls under suitable conditions. However, the great diversity of materials and fabrication techniques has resulted in a huge parameter space significantly complicating the…
Brain representations of curvature may be formed on the basis of either vision or touch. Experimental and theoretical work by the author and her colleagues has shown that the processing underlying such representations directly depends on…
We investigate the influence of curvature and topology on crystalline wrinkling patterns in generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal…
By reformulating Wang tiles with tensors, we propose a natural generalization to the probabilistic and quantum setting. In this new framework, we introduce notions of tilings and periodicity directly extending their classical counterparts.…
Applying constant tensile stress to a piece of amorphous solid results in a slow extension, followed by an eventual rapid mechanical collapse. This "creep" process is of paramount engineering concern, and as such was the subject of study in…
In this paper, the $q$-th dual curvature measure is extended to convex functions and the associated Minkowski problem is posed. A special case includes the $q$-th dual curvature measure of convex bodies which defined by Huang, Lutwak, Yang…
Dislocations in ceramics have enjoyed a long yet underappreciated research history. This brief historical overview and reflection on the current challenges provides new insights into using this line defect as a rediscovered tool for…
A discrete-time Quantum Walk (QW) is an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QW admit, as their continuum limit, a well-known equation of Physics. In arXiv:1803.01015 the QW is…
We show that the entanglement between the internal (spin) and external (position) degrees of freedom of a qubit in a random (dynamically disordered) one-dimensional discrete time quantum random walk (QRW) achieves its maximal possible value…
We consider the evolution and decay of Q-balls under the influence of quantum fluctuations. We argue that the most important effect resulting from these fluctuations is the modification of the effective potential in which the Q-ball…
We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…
NP problems are closely related to practical optimization challenges but often suffer from exponential increases in computation time as problem sizes grow. Quantum annealing offers a promising approach to solve NP problems faster than…
This is the second article of a sequence of research on deformations of Q-curvature. In the previous one, we studied local stability and rigidity phenomena of Q-curvature. In this article, we mainly investigate the volume comparison with…
Quantum walk (QW) provides a versatile tool to study fundamental physics and also to make a variety of practical applications. We here start with the recent idea of {\it nonlinear} QW and show that introducing {\it nonlinearity} to QW can…
The exact cover problem is an NP-complete problem with broad applications. Studies show that although applying the Quantum Approximate Optimization Algorithm (QAOA) to this problem can yield improved solution quality with deeper circuit…
This Letter investigates the formation of quantum droplets in curved spacetime, highlighting the significant influence of curvature on the formation and properties of these objects. While our computations encompass various dimensions, we…
We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both…
Existing mapped WENO schemes can hardly prevent spurious oscillations while preserving high resolutions at long output times. We reveal in this paper the essential reason for such phenomena. It is actually caused by that the mapping…