On nonlinear conservation laws with a nonlocal diffusion term

AbstractScalar one-dimensional conservation laws with a nonlocal diffusion term corresponding to a Riesz–Feller differential operator are considered. Solvability results for the Cauchy problem in L∞ are adapted from the case of a fractional derivative with homogeneous symbol. The main interest of this work is the investigation of smooth shock profiles. In the case of a genuinely nonlinear smooth flux function we prove the existence of such travelling waves, which are monotone and satisfy the standard entropy condition. Moreover, the dynamic nonlinear stability of the travelling waves under small perturbations is proven, similarly to the case of the standard diffusive regularisation, by constructing a Lyapunov functional

Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

Impact of snow state variation for design flood simulations in glacierized catchments

A continuously running hydrological energy balance model was used to analyse the influence of different snow covers on the formation of large floods within glacierized catchments. Model outputs from three different catchments in the Austrian Alps with glacierizations ranging from 30 to 39% were statistically interpreted to cover a wide range of possible combinations of areal snow cover distribution and mean snow water equivalent (SWE_m) and to define initialisation values for extreme runoff scenarios. These model states consider snow conditions between less than 10% snow coverage up to almost complete snow coverage, with different snow depths represented by minimum, mean or maximum levels of SWE_m. For the utilization of extreme runoffs, these snow cover states were combined with design storm input data. An analysis of the resulting flood hydrographs showed that the maximum runoff values occur with minimal snow cover conditions. With increasing snow coverage and SWE_m, flow magnitudes tend to decrease while the relevant precipitation time increases significantly. The influence of topographical catchment features, snow cover and SWE_m on the simulated scenario discharge is discussed. The contribution of the different runoff components to the modelled peak flows confirms the assumption that floods in glacierized catchments are a combination of directly discharging rain and ice melt

Performance of foundation-owned firms in Germany: The role of foundation purpose, stock market listing, and family involvement

To address succession issues, the owners of family firms increasingly transfer their equity to family and charitable foundations, thereby creating so-called foundation-owned firms. This form of succession has become increasingly common in various European countries. A small yet insightful stream of research has emerged comparing the performance of foundation-owned firms against the performance of nonfoundation-owned firms. Our study goes one step further and accounts for the heterogeneous nature of foundation-owned firms. We investigate the role of foundation purpose (family versus charitable foundation), stock market listing, and family involvement. Our results show that firms owned by a family foundation have better accounting performance than firms owned by a charitable foundation. We further find a performance-enhancing effect of family involvement in the firm's management or supervisory board. Contrary to our expectations, we did not observe significant performance differences between private and stock market-listed foundation-owned firms. Our study advances the emergent stream of the foundation-owned (family) firm literature by integrating research on foundation-owned firms with research on family firms. Furthermore, we contribute to the corporate governance literature on ownership effects and blockholder ownership

Hydrological modelling of glacierized catchments focussing on the validation of simulated snow patterns – applications within the flood forecasting system of the Tyrolean river Inn

The catchment of the river Inn is located in the Swiss and Austrian Alps. In the frame of the flood forecasting system "HoPI" (Hochwasserprognose für den Tiroler Inn), the Austrian part of the river Inn and its tributaries are covered within a hybrid numerical model. The runoff from the glacierized headwaters of the south-western Inn tributaries is calculated using the Snow- and Icemelt Model "SES" which utilizes a spatially-distributed energy balance approach; within SES, the accumulation and melting processes for snow, firn, and ice are considered. It is of great importance that such a type of model is used in the simulation of alpine areas since in these regions stream flow is influenced by the accumulation and melt of snow and ice and snow-free glaciers have also the potential to increase or even induce flood flow. For a prototype of the forecast system, SES was calibrated using the snow depletion of a glacier, but later, following the first results during the operational mode, the model was recalibrated and validated using remotely-sensed data covering all 13 glacierized catchments. Using the final snow-parameter setting, a simulation run of 15 hydrological years without any state corrections achieved overall agreements between observed and simulated snow cover ranging from 68% to 88% for all individual catchments. Runoff was calibrated and validated using the data from three different gauges. A parameter set, including both validated snow and runoff parameters, was applied for the modelling of a fourth gauged catchment and also achieved accurate results. This final unique parameterization was transferred to the remaining, ungauged watersheds

Foundation ownership and shareholder value: an event study

Some of the largest listed firms in Western and Northern Europe are partly owned by foundations. So far, little research exists about the shareholder value effects of foundation ownership. This study aims to close this gap using an event study method. We find that equity markets show a positive reaction following the announcement by a foundation that it intends to decrease its ownership share, whereas we find no reaction when a foundation announces that it intends to increase its ownership share. The positive reaction to an announcement of an ownership share decrease is particularly strong when a foundation holds an equity stake of less than 25%. Further investigations show that our findings are specific for foundations as blockholders and do not occur with other blockholders. Overall, our study s

Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects

In this paper we propose and study a new kinetic rating model for a large number of players, which is motivated by the well-known Elo rating system. Each player is characterised by an intrinsic strength and a rating, which are both updated after each game. We state and analyse the respective Boltzmann type equation and derive the corresponding nonlinear, nonlocal Fokker-Planck equation. We investigate the existence of solutions to the Fokker-Planck equation and discuss their behaviour in the long time limit. Furthermore, we illustrate the dynamics of the Boltzmann and Fokker-Planck equation with various numerical experiments

PPA2-associated sudden cardiac death: extending the clinical and allelic spectrum in 20 new families

Purpose: Biallelic hypomorphic variants in PPA2, encoding the mitochondrial inorganic pyrophosphatase 2 protein, have been recently identified in individuals presenting with sudden cardiac death, occasionally triggered by alcohol intake or a viral infection. Here we report 20 new families harboring PPA2 variants. Methods: Synthesis of clinical and molecular data concerning 34 individuals harboring five previously reported PPA2 variants and 12 novel variants, 11 of which were functionally characterized. Results: Among the 34 individuals, only 6 remain alive. Twenty-three died before the age of 2 years while five died between 14 and 16 years. Within these 28 cases, 15 died of sudden cardiac arrest and 13 of acute heart failure. One case was diagnosed prenatally with cardiomyopathy. Four teenagers drank alcohol before sudden cardiac arrest. Progressive neurological signs were observed in 2/6 surviving individuals. For 11 variants, recombinant PPA2 enzyme activities were significantly decreased and sensitive to temperature, compared to wild-type PPA2 enzyme activity. Conclusion: We expand the clinical and mutational spectrum associated with PPA2 dysfunction. Heart failure and sudden cardiac arrest occur at various ages with inter- and intrafamilial phenotypic variability, and presentation can include progressive neurological disease. Alcohol intake can trigger cardiac arrest and should be strictly avoided.Anne Guimier ... Liza K. Phillips ... et al

Degradation of Host Sphingomyelin Is Essential for Leishmania Virulence

In eukaryotes, sphingolipids (SLs) are important membrane components and powerful signaling molecules. In Leishmania, the major group of SLs is inositol phosphorylceramide (IPC), which is common in yeast and Trypanosomatids but absent in mammals. In contrast, sphingomyelin is not synthesized by Leishmania but is abundant in mammals. In the promastigote stage in vitro, Leishmania use SL metabolism as a major pathway to produce ethanolamine (EtN), a metabolite essential for survival and differentiation from non-virulent procyclics to highly virulent metacyclics. To further probe SL metabolism, we identified a gene encoding a putative neutral sphingomyelinase (SMase) and/or IPC hydrolase (IPCase), designated ISCL (Inositol phosphoSphingolipid phospholipase C-Like). Despite the lack of sphingomyelin synthesis, L. major promastigotes exhibited a potent SMase activity which was abolished upon deletion of ISCL, and increased following over-expression by episomal complementation. ISCL-dependent activity with sphingomyelin was about 20 fold greater than that seen with IPC. Null mutants of ISCL (iscl−) showed modest accumulation of IPC, but grew and differentiated normally in vitro. Interestingly, iscl− mutants did not induce lesion pathology in the susceptible BALB/c mice, yet persisted indefinitely at low levels at the site of infection. Notably, the acute virulence of iscl− was completely restored by the expression of ISCL or heterologous mammalian or fungal SMases, but not by fungal proteins exhibiting only IPCase activity. Together, these findings strongly suggest that degradation of host-derived sphingomyelin plays a pivotal role in the proliferation of Leishmania in mammalian hosts and the manifestation of acute disease pathology