We analyze the quantum ground state structure of a specific model of itinerant, strongly interacting lattice fermions. The interactions are tuned to make the model supersymmetric. Due to this, quantum ground states are in one-to-one correspondence with cohomology classes of the so-called independence complex of the lattice. Our main result is a complete description of the cohomology, and thereb...

Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical surface stresses on the body. Moreover, these inaccurate stresses often lead to unphysical oscillations in the history of integrated surface forces such as the ...

The cochlea or inner ear has a remarkable ability to amplify sound signals. This is understood to derive at least in part from some active process that magnifies vibrations of the basilar membrane (BM) and the cochlear partition in which it is embedded, to the extent that it overcomes the effect of viscous damping from the surrounding cochlear fluid. Many authors have associated this amplificat...

We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives. It ...

In this work we consider how surface-adherent bacterial biofilm communities respond in flowing systems. We simulate the fluid-structure interaction and separation process using the immersed boundary method. In these simulations we model and simulate different density and viscosity values of the biofilm than that of the surrounding fluid. The simulation also includes breakable springs connecting...

of Paper The paper presents an algorithm for physically accurate simulation of elastic deformable objects that are also fast enough for real-time animation. The algorithm uses Boundary Element Method (BEM) (vs. Finite Element Method). The algorithm applies to deformable objects that can be simulated by linear elastic models. It achieves interactive speeds by exploiting coherence in typical inte...

We analyse supermembrane instantons (fully wrapped supermembranes) by computing the partition function of the three-dimensional supersymmetrical U(N) matrix model under periodic boundary conditions. By mapping the model to a cohomological field theory and considering a mass-deformation of the model, we show that the partition function exactly leads to the U-duality invariant measure factor ente...

A one-dimensional system of masses with nearest-neighbor interactions and periodic boundary conditions is used to study mode decay and ergodicity in nonlinear, disordered systems. The system is given an initial periodic displacement, and the total system energy within a specific frequency channel is measured as a function of time. Results indicate that the rate of mode decay at early times incr...

Coarse-grained models of soft matter are usually combined with implicit solvent models that take the electrostatic polarizability into account via a dielectric background. In biophysical or nanoscale simulations that include water, this constant can vary greatly within the system. Performing molecular dynamics or other simulations that need to compute exact electrostatic interactions between ch...

A treecode algorithm is presented for computing the electrostatic potential and electric field in a system of charged particles. The algorithm is grid-free and with N particles it reduces the operation count to O(N logN), as opposed to O(N2) which is required for direct summation of pairwise interactions. The key idea is to replace the particle–particle interactions by particle– cluster interac...