Environmental carcinogens, such as polycyclic aromatic hydrocarbons (PAHs), require metabolic activation to DNA-reactive metabolites in order to exert their tumorigenic effects. Benzo[a]pyrene (B[a]P), a prototypic PAH, is metabolized by cytochrome P450 (P450) 1A1/1B1 and epoxide hydrolase to (-)-B[a]P-7,8-dihydro-7,8-diol (B[a]P-7,8-dihydrodiol). B[a]P-7,8-dihydrodiol then undergoes further P4...

We present a two-level parameterized Model Order Reduction (pMOR) technique for the linear hyperbolic Partial Differential Equation (PDE) of time-domain elastodynamics. In order to approximate frequency-domain PDE, we take advantage Port-Reduced Reduced-Basis Component (PR-RBC) method develop (in offline stage) reduced bases subdomains; latter are then assembled online form global domains inter...

In this paper we describe an interactive symbolic-numericinterfaceframework (editor) to the ELLPACK partial diierential equation (PDE) system for building PDE solvers for a much broader range of applications. The domain of applicability of ELLPACK and its parallel version (//ELLPACK) is restricted to second order linear elliptic boundary value problems. This editor allows the speciication of no...

The formation of finite time singularities in a nonlinear parabolic fourth order partial differential equation (PDE) is investigated for a variety of two-dimensional geometries. The PDE is a variant of a canonical model for Micro-Electro Mechanical systems (MEMS). The singularities are observed to form at specific points in the domain and correspond to solutions whose values remain finite but w...

In this paper it is shown that the characteristic vector field associated to a first order PDE: h(x,∇z(x)) = 0 with x ∈ Rn has the same form of an infinitesimal generator of an odd-symplectic transformation with contact Hamiltonian h(x, p) on the level set h = 0. We also study under which condition such PDE has a characteristic vector field commuting with a generator of an odd-symplectic action.

In this paper we study a nonlinear system of differential equations which arises from a stationary 2-dimensional Ice-Sheet Model describing the ice-streaming phenomenon. The system consists of a multivalued nonlinear PDE of parabolic type coupled with a first order PDE and an ODE involving a nonlocal term. We study the uniqueness of weak solution under suitable assumptions (physically reasonabl...

We show the short-time existence and uniqueness of solutions for the motion of an evolving hypersurface in contact with a solid container driven by the volume-preserving mean curvature flow (MCF) taking line tension effects on the boundary into account. Difficulties arise due to dynamic boundary conditions and due to the contact angle and the non-local nature of the resulting second order, nonl...

In the recent B̂ılă’s paper [1] it was determined the symmetry group of the minimal surfaces PDE (using classical methods). The aim of this paper is to find the Lie algebra of contact symmetries of the minimal surfaces PDE using the correspondence, established by V. V. Lychagin [2], between the second order non-linear differential operators and differential forms which are given on the manifold ...

This paper is concerned with computing very high order accurate linear functionals from a numerical solution of a time-dependent partial differential equation (PDE). Based on finite differences on summation-by-parts form, together with a weak implementation of the boundary conditions, we show how to construct suitable boundary conditions for the PDE such that the continuous problem is well-pose...

Anti-self-dual metrics in the (+ +−−) signature which admit a covariantly constant real spinor are studied. It is shown that finding such metrics reduces to solving a fourth order integrable PDE, and some examples are given. The corresponding twistor space is characterised by existence of an anti-canonical rank-one divisor line bundle. It is demonstrated that if the parallel spinor is preserved...