Related papers: Fingered growth in channel geometry: A Loewner equ…
We investigate to what degree the steady laminar flow in typical micro- and mini-channels with offset strip fin arrays can be described as developed on a macro-scale level, in the presence of channel entrance and side-wall effects. Hereto,…
In a recent paper, we exhibit a link between the average local growth of Laplace eigenfunctions on surfaces and the size of their nodal set. In that paper, the average local growth is computed using the uniform - or $L^\infty$ - growth…
Many alternative formulations of Einstein's evolution have lately been examined, in an effort to discover one which yields slow growth of constraint-violating errors. In this paper, rather than directly search for well-behaved formulations,…
We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of…
Capillary fingering is a displacement process that can occur when a non-wetting fluid displaces a wetting fluid from a homogeneous disordered porous medium. Here, we investigate how this process is influenced by a pore size gradient. Using…
Let R be a hyperbolic Riemann surface with boundary $\partial R$ and suppose that $\gamma:[0,T]\to R\cup\partial R$ is a simple curve growing from the boundary of R. By lifting $R_{t}=R\setminus \gamma(0,t]$ to the universal covering space…
A new model of Laplacian stochastic growth is formulated using conformal mappings. The model describes two growth regimes, stable and turbulent, separated by a sharp phase transition. The first few Fourier components of the mapping define…
The dynamical generation of right-handed-neutrino (RHN) masses in the early Universe naturally entails the formation of cosmic strings that give rise to an observable signal in gravitational waves (GWs). Here, we show that a characteristic…
Double-diffusive instabilities are often invoked to explain enhanced transport in stably-stratified fluids. The most-studied natural manifestation of this process, fingering convection, commonly occurs in the ocean's thermocline and…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
Let $(M,g)$ be a smooth, compact, Riemannian manifold and $\{\phi_h\}$ a sequence of $L^2$-normalized Laplace eigenfunctions on $M$. For a smooth submanifold $H\subset M$, we consider the growth of the restricted eigenfunctions $\phi_h|_H$…
A growth of malignant neoplasm is considered as a fractional transport approach. We suggested that the main process of the tumor development through a lymphatic net is fractional transport of cells. In the framework of this fractional…
The growth exponent $\alpha$ for loop-erased or Laplacian random walk on the integer lattice is defined by saying that the expected time to reach the sphere of radius $n$ is of order $n^\alpha$. We prove that in two dimensions, the growth…
Natural evolution has produced a tremendous diversity of functional organisms. Many believe an essential component of this process was the evolution of evolvability, whereby evolution speeds up its ability to innovate by generating a more…
We present a theoretical study for the intermediate stages of the growth of membranes and vesicles in supersaturated solutions of amphiphilic molecules. The problem presents important differences with the growth of droplets in the classical…
In this paper, we define and study Loewner chains and evolution families on finitely multiply-connected domains in the complex plane. These chains and families consist of conformal mappings on parallel slit half-planes and have one and two…
We investigate the formation of fingered flow in dry granular media under simulated rainfall using a quasi-2D experimental set-up composed of a random close packing of mono-disperse glass beads. Using controlled experiments, we analyze the…
Graphs with diverse structural characteristics play a central role in modelling and optimization tasks. The ability to generate different types of graphs that exhibit shared properties is likewise essential for algorithm selection and…
We study the effect of acceleration and deceleration on the stability of channel flows. To do so, we derive an exact solution for laminar profiles of channel flows with arbitrary, time-varying wall motion and pressure gradient. This…
We report a new algorithm to generate Laplacian Growth Patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth…