BKM Lie superalgebras from counting twisted CHL dyons

Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M_{24}, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the dd-modular forms, that have been classified by Clery and Gritsenko[arXiv:0812.3962]. We show that each one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the walls of marginal stability in the corresponding CHL model for twisted dyons as well as untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that are consistent with physical expectations.Comment: LaTeX, 32 pages; (v2) matches published versio

INVESTIGATION OF DISCRETE POPULATION BALANCE MODELS AND ITS PARAMETERS FOR TURBULENT EMULSIFICATION PRO- CESSES

Abstract. Different challenges and limitations occur with the simulation of liquid/liquid dispersion using population balance equations (PBE). A limitation is that the breakage and coalescence kernels tend to be specific to the equipment and scale used to acquire the evaluation data. It is reported in literature that PBE simulations are highly scale dependent. Once information is obtained using PBE, it cannot be used, with confidence, for scale-u

Micro-plasticity and intermittent dislocation activity in a simplified micro structural model

Here we present a model to study the micro-plastic regime of a stress-strain curve. In this model an explicit dislocation population represents the mobile dislocation content and an internal shear-stress field represents a mean-field description of the immobile dislocation content. The mobile dislocations are constrained to a simple dipolar mat geometry and modelled via a dislocation dynamics algorithm, whilst the shear-stress field is chosen to be a sinusoidal function of distance along the mat direction. The latter, defined by a periodic length and a shear-stress amplitude, represents a pre-existing micro-structure. These model parameters, along with the mobile dislocation density, are found to admit a diversity of micro-plastic behaviour involving intermittent plasticity in the form of a scale-free avalanche phenomenon, with an exponent for the strain burst magnitude distribution similar to those seen in experiment and more complex dislocation dynamics simulations.Comment: 30 pages, 12 figures, to appear in "Modelling and Simulation in Materials Science and Engineering

Monitoring global protein thiol-oxidation and protein S-mycothiolation in Mycobacterium smegmatis under hypochlorite stress.

Hillion M, Bernhardt J, Busche T, et al. Monitoring global protein thiol-oxidation and protein S-mycothiolation in Mycobacterium smegmatis under hypochlorite stress. Sci Rep. 2017;7(1): 1195.Mycothiol (MSH) is the major low molecular weight (LMW) thiol in Actinomycetes. Here, we used shotgun proteomics, OxICAT and RNA-seq transcriptomics to analyse protein S-mycothiolation, reversible thiol-oxidations and their impact on gene expression in Mycobacterium smegmatis under hypochlorite stress. In total, 58 S-mycothiolated proteins were identified under NaOCl stress that are involved in energy metabolism, fatty acid and mycolic acid biosynthesis, protein translation, redox regulation and detoxification. Protein S-mycothiolation was accompanied by MSH depletion in the thiol-metabolome. Quantification of the redox state of 1098 Cys residues using OxICAT revealed that 381 Cys residues (33.6%) showed >10% increased oxidations under NaOCl stress, which overlapped with 40 S-mycothiolated Cys-peptides. The absence of MSH resulted in a higher basal oxidation level of 338 Cys residues (41.1%). The RseA and RshA anti-sigma factors and the Zur and NrdR repressors were identified as NaOCl-sensitive proteins and their oxidation resulted in an up-regulation of the SigH, SigE, Zur and NrdR regulons in the RNA-seq transcriptome. In conclusion, we show here that NaOCl stress causes widespread thiol-oxidation including protein S-mycothiolation resulting in induction of antioxidant defense mechanisms in M. smegmatis. Our results further reveal that MSH is important to maintain the reduced state of protein thiols

Generalized Kac-Moody Algebras from CHL dyons

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6), (3,4), and possibly (5,2). The square of the automorphic form is the modular transform of the generating function of the degeneracy of CHL dyons in asymmetric Z_N-orbifolds of the heterotic string compactified on T^6. The new generalized Kac-Moody superalgebras all arise as different `automorphic corrections' of the same Lie algebra and are closely related to a generalized Kac-Moody superalgebra constructed by Gritsenko and Nikulin. The automorphic forms, Delta_{k/2}(Z), arise as additive lifts of Jacobi forms of (integral) weight k/2 and index 1/2. We note that the orbifolding acts on the imaginary simple roots of the unorbifolded GKM superalgebra, G_1 leaving the real simple roots untouched. We anticipate that these superalgebras will play a role in understanding the `algebra of BPS states' in CHL compactifications.Comment: LaTeX, 35 pages; v2: improved referencing and discussion; typos corrected; v3 [substantial revision] 44 pages, modularity of additive lift proved, product representation of the forms also given; further references adde