Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells I

We describe the asymptotic of the steady states of the out-of equilibrium Schrödinger-Poisson system, in the regime of quantum wells in a semiclassical island. After establishing uniform estimates on the nonlinearity, we show that the nonlinear steady states lie asymptotically in a finite-dimensional subspace of functions and that the involved spectral quantities are reduced to a finite number of so-called asymptotic resonant energies. The asymptotic finite dimensional nonlinear system is written in a general setting with only a partial information on its coefficients. After this first part, a complete derivation of the asymptotic nonlinear system will be done for some specific cases in a forthcoming article. UNE VERSION MODIFIEE DE CE TEXTE EST PARUE DANS LES ANNALES DE L'INSTITUT H. POINCARE, ANALYSE NON LINEAIRE

Tissue fusion over non-adhering surfaces

Tissue fusion eliminates physical voids in a tissue to form a continuous structure and is central to many processes in development and repair. Fusion events in vivo, particularly in embryonic development, often involve the purse-string contraction of a pluricellular actomyosin cable at the free edge. However in vitro, adhesion of the cells to their substrate favors a closure mechanism mediated by lamellipodial protrusions, which has prevented a systematic study of the purse-string mechanism. Here, we show that monolayers can cover well-controlled mesoscopic non-adherent areas much larger than a cell size by purse-string closure and that active epithelial fluctuations are required for this process. We have formulated a simple stochastic model that includes purse-string contractility, tissue fluctuations and effective friction to qualitatively and quantitatively account for the dynamics of closure. Our data suggest that, in vivo, tissue fusion adapts to the local environment by coordinating lamellipodial protrusions and purse-string contractions

Vortex distribution in the Lowest Landau Level

We study the vortex distribution of the wave functions minimizing the Gross Pitaevskii energy for a fast rotating condensate in the Lowest Landau Level (LLL): we prove that the minimizer cannot have a finite number of zeroes thus the lattice is infinite, but not uniform. This uses the explicit expression of the projector onto the LLL. We also show that any slow varying envelope function can be approximated in the LLL by distorting the lattice. This is used in particular to approximate the inverted parabola and understand the role of ``invisible'' vortices: the distortion of the lattice is very small in the Thomas Fermi region but quite large outside, where the "invisible" vortices lie.Comment: 4 pages, 1 figur

Simulation of resonant tunneling heterostructures: numerical comparison of a complete Schr{ö}dinger-Poisson system and a reduced nonlinear model

Two different models are compared for the simulation of the transverse electronic transport through an heterostructure: a $1D$ self-consistent Schr{ö}dinger-Poisson model with a numerically heavy treatment of resonant states and a reduced model derived from an accurate asymptotic nonlinear analysis. After checking the agreement at the qualitative and quantitative level on quite well understood bifurcation diagrams, the reduced model is used to tune double well configurations for which nonlinearly interacting resonant states actually occur in the complete self-consistent model

Densely Entangled Financial Systems

In [1] Zawadoski introduces a banking network model in which the asset and counter-party risks are treated separately and the banks hedge their assets risks by appropriate OTC contracts. In his model, each bank has only two counter-party neighbors, a bank fails due to the counter-party risk only if at least one of its two neighbors default, and such a counter-party risk is a low probability event. Informally, the author shows that the banks will hedge their asset risks by appropriate OTC contracts, and, though it may be socially optimal to insure against counter-party risk, in equilibrium banks will {\em not} choose to insure this low probability event. In this paper, we consider the above model for more general network topologies, namely when each node has exactly 2r counter-party neighbors for some integer r>0. We extend the analysis of [1] to show that as the number of counter-party neighbors increase the probability of counter-party risk also increases, and in particular the socially optimal solution becomes privately sustainable when each bank hedges its risk to at least n/2 banks, where n is the number of banks in the network, i.e., when 2r is at least n/2, banks not only hedge their asset risk but also hedge its counter-party risk.Comment: to appear in Network Models in Economics and Finance, V. Kalyagin, P. M. Pardalos and T. M. Rassias (editors), Springer Optimization and Its Applications series, Springer, 201

Unequal allelic expression of wild-type and mutated β-myosin in familial hypertrophic cardiomyopathy

Familial hypertrophic cardiomyopathy (FHC) is an autosomal dominant disease, which in about 30% of the patients is caused by missense mutations in one allele of the β-myosin heavy chain (β-MHC) gene (MYH7). To address potential molecular mechanisms underlying the family-specific prognosis, we determined the relative expression of mutant versus wild-type MYH7-mRNA. We found a hitherto unknown mutation-dependent unequal expression of mutant to wild-type MYH7-mRNA, which is paralleled by similar unequal expression of β-MHC at the protein level. Relative abundance of mutated versus wild-type MYH7-mRNA was determined by a specific restriction digest approach and by real-time PCR (RT-qPCR). Fourteen samples from M. soleus and myocardium of 12 genotyped and clinically well-characterized FHC patients were analyzed. The fraction of mutated MYH7-mRNA in five patients with mutation R723G averaged to 66 and 68% of total MYH7-mRNA in soleus and myocardium, respectively. For mutations I736T, R719W and V606M, fractions of mutated MYH7-mRNA in M. soleus were 39, 57 and 29%, respectively. For all mutations, unequal abundance was similar at the protein level. Importantly, fractions of mutated transcripts were comparable among siblings, in younger relatives and unrelated carriers of the same mutation. Hence, the extent of unequal expression of mutated versus wild-type transcript and protein is characteristic for each mutation, implying cis-acting regulatory mechanisms. Bioinformatics suggest mRNA stability or splicing effectors to be affected by certain mutations. Intriguingly, we observed a correlation between disease expression and fraction of mutated mRNA and protein. This strongly suggests that mutation-specific allelic imbalance represents a new pathogenic factor for FHC

Deducing the source and composition of rare earth mineralising fluids in carbonatites: insights from isotopic (C, O, 87Sr/86Sr) data from Kangankunde, Malawi

This is the final version of the article. Available from Springer Verlag via the DOI in this record.Carbonatites host some of the largest and highest grade rare earth element (REE) deposits but the composition and source of their REE-mineralising fluids remains enigmatic. Using C, O and 87Sr/86Sr isotope data together with major and trace element compositions for the REE-rich Kangankunde carbonatite (Malawi), we show that the commonly observed, dark brown, Fe-rich carbonatite that hosts REE minerals in many carbonatites is decoupled from the REE mineral assemblage. REE-rich ferroan dolomite carbonatites, containing 8–15 wt% REE2O3, comprise assemblages of monazite-(Ce), strontianite and baryte forming hexagonal pseudomorphs after probable burbankite. The 87Sr/86Sr values (0.70302–0.70307) affirm a carbonatitic origin for these pseudomorph-forming fluids. Carbon and oxygen isotope ratios of strontianite, representing the REE mineral assemblage, indicate equilibrium between these assemblages and a carbonatite-derived, deuteric fluid between 250 and 400 °C (δ18O + 3 to + 5‰VSMOW and δ13C − 3.5 to − 3.2‰VPDB). In contrast, dolomite in the same samples has similar δ13C values but much higher δ18O, corresponding to increasing degrees of exchange with low-temperature fluids (< 125 °C), causing exsolution of Fe oxides resulting in the dark colour of these rocks. REE-rich quartz rocks, which occur outside of the intrusion, have similar δ18O and 87Sr/86Sr to those of the main complex, indicating both are carbonatite-derived and, locally, REE mineralisation can extend up to 1.5 km away from the intrusion. Early, REE-poor apatite-bearing dolomite carbonatite (beforsite: δ18O + 7.7 to + 10.3‰ and δ13C −5.2 to −6.0‰; 87Sr/86Sr 0.70296–0.70298) is not directly linked with the REE mineralisation.This project was funded by the UK Natural Environment Research Council (NERC) SoS RARE project (NE/M011429/1) and by NIGL (NERC Isotope Geoscience Laboratory) Project number 20135

Banks’ liquidity buffers and the role of liquidity regulation

We assess the determinants of banks’ liquidity holdings using data for nearly 7000 banks from 25 OECD countries. We highlight the role of several bank-specific, institutional and policy variables in shaping banks’ liquidity risk management. Our main question is whether liquidity regulation neutralizes banks’ incentives to hold liquid assets. Without liquidity regulation, the determinants of banks’ liquidity buffers are a combination of bank-specific and country-specific variables. While most incentives are neutralized by liquidity regulation, a bank’s disclosure requirements remain important. The complementarity of disclosure and liquidity requirements provides a strong rationale for considering them jointly in the design of regulation