Related papers: A particular case of a Lifting Hele-Shaw Cell
Magic state distillation protocols have a complicated non-linear nature. Analysis of protocols is therefore usually restricted to one-parameter families of states, which aids tractability. We show that if we lift this one-parameter…
We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information on lex segment ideals. Moreover, we introduce a numerical functions…
We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase.…
We develop methods to obtain the fully differential cross-section for the $f \bar{f} \to Z(\ell\ell)\,h$ process to any desired order in effective field theory (EFT). To achieve this, we first derive a mapping between the partial wave…
Imposing a strong condition on the linear order of shellable complexes, we introduce strong shellability. Basic properties, including the existence of dimension-decreasing strong shelling orders, are developed with respect to nonpure…
Tensoring finite pointed simplicial sets with commutative ring spectra yields important homology theories such as (higher) topological Hochschild homology and torus homology. We prove several structural properties of these constructions…
We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in particular a hybrid based on the $3$-level Sierpinski…
We studied the photoelectron spectra generated by an intense few-cycle infrared laser pulse. By focusing on the angular distributions of the back rescattered high energy photoelectrons, we show that accurate differential elastic scattering…
A hierarchy of mathematical models describing viscosity-stratified flow in a Hele-Shaw cell is constructed. Numerical modelling of jet flow and development of viscous fingers with the influence of inertia and friction is carried out.…
The surface partition of large fragments is derived analytically within a simple statistical model by the Laplace-Fourier transformation method. In the limit of small amplitude deformations, a suggested Hills and Dales Model reproduces the…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
A bent crystal shield which is capable of deflecting cosmic radiation ions of all atomic numbers away from spacecraft using the ion channeling effect is described. Its effect on the transmitted angular distribution of heavy, high-energy…
We introduce "fractalization", a procedure by which spin models are extended to higher-dimensional "fractal" spin models. This allows us to interpret type-II fracton phases, fractal symmetry-protected topological phases, and more, in terms…
Ultrafast imaging of molecular chirality is a key step towards the dream of imaging and interpreting electronic dynamics in complex and biologically relevant molecules. Here, we propose a new ultrafast chiral phenomenon exploiting recent…
The segmentation of cell nuclei in tissue images stained with the blood dye hematoxylin and eosin (H$\&$E) is essential for various clinical applications and analyses. Due to the complex characteristics of cellular morphology, a large…
We explain how a single scalar degree of freedom can be obtained from projecting out all the other components of a chiral superfield using simple operators in the microscopic theory. We use the Fayet-Iliopoulos model as an example of the…
We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.
We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right…
In this short note, we construct some nontrivial examples of topological biquandle. The key ingredient of the construction is the notion of skew brace.
Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the…