Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

Quadratic BSDEs with convex generators and unbounded terminal conditions

In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context

Kinetic theory model predictions compared with low-thrust axisymmetric nozzle plume data

A system of nonlinear integral equations equivalent to the steady-state Krook kinetic equation was used to model the flow from a low-thrust axisymmetric nozzle. The mathematical model was used to numerically calculate the number density, temperature, and velocity of a simple gas as it expands into a near vacuum. With these quantities the gas pressure and flow directions of the gas near the exit plane were calculated and compared with experimental values for a low-thrust nozzle of the same geometry and mass flow rate

Extreme magnetic field-boosted superconductivity

Applied magnetic fields underlie exotic quantum states, such as the fractional quantum Hall effect and Bose-Einstein condensation of spin excitations. Superconductivity, on the other hand, is inherently antagonistic towards magnetic fields. Only in rare cases can these effects be mitigated over limited fields, leading to reentrant superconductivity. Here, we report the unprecedented coexistence of multiple high-field reentrant superconducting phases in the spin-triplet superconductor UTe2. Strikingly, we observe superconductivity in the highest magnetic field range identified for any reentrant superconductor, beyond 65 T. These extreme properties reflect a new kind of exotic superconductivity rooted in magnetic fluctuations and boosted by a quantum dimensional crossover