Scaling behavior of the conserved transfer threshold process

We analyze numerically the critical behavior of an absorbing phase transition in the conserved transfer threshold process. We determined the steady state scaling behavior of the order parameter as a function of both, the control parameter and an external field, conjugated to the order parameter. The external field is realized as a spontaneous creation of active particles which drives the system away from criticality. The obtained results yields that the conserved transfers threshold process belongs to the universality class of absorbing phase transitions in a conserved field.Comment: 6 pages, 8 figures, accepted for publication in Phys. Rev.

A Murnaghan--Nakayama rule for values of unipotent characters in classical groups

We derive a Murnaghan--Nakayama type formula for the values of unipotent characters of finite classical groups on regular semisimple elements. This relies on Asai's explicit decomposition of Lusztig restriction. We use our formula to show that most complex irreducible characters vanish on some $\ell$-singular element for certain primes $\ell$. As an application we classify the simple endotrivial modules of the finite quasi-simple classical groups. As a further application we show that for finite simple classical groups and primes $\ell\ge3$ the first Cartan invariant in the principal $\ell$-block is larger than~2 unless Sylow $\ell$-subgroups are cyclic.Comment: Added a missing assumption to the statement of theorem 2. 25.11.16: Added a corrigendum to the proof of Thm. 7.

On defining characteristic representations of finite reductive groups

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic

Mean-field scaling function of the universality class of absorbing phase transitions with a conserved field

We consider two mean-field like models which belong to the universality class of absorbing phase transitions with a conserved field. In both cases we derive analytically the order parameter as function of the control parameter and of an external field conjugated to the order parameter. This allows us to calculate the universal scaling function of the mean-field behavior. The obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five and six dimensional models, showing that four is the upper critical dimension of this particular universality class.Comment: 8 pages, 2 figures, accepted for publication in J. Phys.

Randmoness and Step-like Distribution of Pile Heights in Avalanche Models

The paper develops one-parametric family of the sand-piles dealing with the grains' local losses on the fixed amount. The family exhibits the crossover between the models with deterministic and stochastic relaxation. The mean height of the pile is destined to describe the crossover. The height's densities corresponding to the models with relaxation of the both types tend one to another as the parameter increases. These densities follow a step-like behaviour in contrast to the peaked shape found in the models with the local loss of the grains down to the fixed level [S. Lubeck, Phys. Rev. E, 62, 6149, (2000)]. A spectral approach based on the long-run properties of the pile height considers the models with deterministic and random relaxation more accurately and distinguishes the both cases up to admissible parameter values.Comment: 5 pages, 5 figure

Rigidity for F_4(p)

We prove the existence of certain rationally rigid triples in F_4(p) for good primes p (i.e., p>3), thereby showing that these groups occur as regular Galois groups over Q(t) and so also over Q. We show that these triples give rise to rigid triples in the algebraic group and prove that they generate an interesting subgroup in characteristic 0.Comment: 9 pages. Welcome comment

Green protein from locally grown crops (OK-Net EcoFeed Practice Abstract)

• Choose an appropriate type of green crop, such as clover-grass or alfalfa, with an expected high protein and amino acid content. Consider soil types and weather patterns to grow a crop with a good and high quality yield. • Harvest the field at regular intervals in order to achieve good plant growth and to obtain batches with more high quality protein and less fibre • Harvesting procedures, which minimise soil content in the green material obtained from the field are necessary to obtain good quality green protein and to avoid wear of machinery and technical equipment • Cooperation with a bio-refinery plant is a prerequisite in order to concentrate the protein into a green paste that can be dried and used in poultry feed. • If not dried, the wet green paste can be stored in closed containers/plastic bags in cool conditions for a shorter period. • Chemical analysis of the green protein concentrate is important in order to replace other protein sources such as soya and to carry out the correct feed formulation. This can be done together with advisors or feed companies