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

Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators

The aim of the present paper is to study the regularity properties of the solution of a backward stochastic differential equation with a monotone generator in infinite dimension. We show some applications to the nonlinear Kolmogorov equation and to stochastic optimal control

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

Symbiotic UCYN-A Strains Co-occurred with El Niño, Relaxed Upwelling, and Varied Eukaryotes Over 10 Years Off Southern California

Biological nitrogen fixation, the conversion of N2 gas into a bioavailable form, is vital to sustaining marine primary production. Studies have shifted beyond traditionally studied tropical diazotrophs. Candidatus Atelocyanobacterium thalassa (or UCYN-A) has emerged as a focal point due to its streamlined metabolism, intimate partnership with a haptophyte host, and broad distribution. Here, we explore the environmental parameters that govern UCYN-A’s presence at the San Pedro Ocean Time-series (SPOT), its host specificity, and statistically significant interactions with non-host eukaryotes from 2008-2018. 16S and 18S rRNA gene sequences were amplified by “universal primers” from monthly samples and resolved into Amplicon Sequence Variants, allowing us to observe multiple UCYN-A symbioses. UCYN-A1 relative abundances increased following the 2015-2016 El Niño event. This “open ocean ecotype” was present when coastal upwelling declined, and Ekman transport brought tropical waters into the region. Network analyses reveal all strains of UCYN-A co-occur with dinoflagellates including Lepidodinium, a potential predator, and parasitic Syndiniales. UCYN-A2 appeared to pair with multiple hosts and was not tightly coupled to its predominant host, while UCYN-A1 maintained a strong host-symbiont relationship. These biological relationships are particularly important to study in the context of climate change, which will alter UCYN-A distribution at regional and global scales

Field-dependent heat transport in the Kondo insulator SmB6 : phonons scattered by magnetic impurities

The thermal conductivity $\kappa$ of the Kondo insulator SmB$_6$ was measured at low temperature, down to 70 mK, in magnetic fields up to 15 T, on single crystals grown using both the floating-zone and the flux methods. The residual linear term $\kappa_0/T$ at $T \to 0$ is found to be zero in all samples, for all magnetic fields, in agreement with previous studies. There is therefore no clear evidence of fermionic heat carriers. In contrast to some prior data, we observe a large enhancement of $\kappa(T)$ with increasing field. The effect of field is anisotropic, depending on the relative orientation of field and heat current (parallel or perpendicular), and with respect to the cubic crystal structure. We interpret our data in terms of heat transport predominantly by phonons, which are scattered by magnetic impurities.Comment: publish versio