The staircase method: integrals for periodic reductions of integrable lattice equations

We show, in full generality, that the staircase method provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the QD-algorithm, and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r<n, then one can introduce q<= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular 2D lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.Comment: 40 pages, 23 Figure

Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I

We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of 2nd order systems with a 3rd order or a 4th order symmetry and 3rd order systems with a 5th order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made.Comment: 60 pages, 6 tables; added one remark in section 4.2.17 (p.33) plus several minor changes, to appear in J.Phys.

Impact of moisture and grinding on yield, physical, chemical and thermal properties of wholegrain flour obtained from hydrothermally treated sorghum grains

The present work evaluates the potential of sorghum with high content of tannins for wholegrain flour production. Two types of mills were used: a roller mill (RM) and a blade (BM) mill. The impact of moisture and grinding on yield, physical, chemical and thermal properties were evaluated. Maximum yield was obtained using a BM with 25% moisture in the grain, resulting in 60.9% versus 28% (g flour g−1 of wholegrain sorghum) for the RM. Grain moisture and milling type affected flour colour and ashes. For both mills, the pasting and thermal properties of flour with grain moisture variation were significantly different from the untreated control sample. By studying the procedures for flour production and quality characteristics, it is possible to produce flour with good physical attributes, which can contribute to the development of gluten‐free foods based on sorghum for the coeliac population.Fil: Acquisgrana, María del Rosario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Química Básica y Aplicada del Nordeste Argentino. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Química Básica y Aplicada del Nordeste Argentino; Argentina. Universidad Tecnológica Nacional. Facultad Regional Resistencia. Departamento de Ingeniería Química. Laboratorio de Química Teórica y Experimental; ArgentinaFil: Gómez Pamies, Laura Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Química Básica y Aplicada del Nordeste Argentino. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Química Básica y Aplicada del Nordeste Argentino; Argentina. Universidad Tecnológica Nacional. Facultad Regional Resistencia. Departamento de Ingeniería Química. Laboratorio de Química Teórica y Experimental; ArgentinaFil: Martinez Amezaga, Nancy María Jimena. Universidad Tecnológica Nacional. Facultad Regional Resistencia. Departamento de Ingeniería Química. Laboratorio de Química Teórica y Experimental; ArgentinaFil: Quiroga, Fernanda Micaela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Ciencia y Tecnología de Alimentos Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Ciencia y Tecnología de Alimentos Córdoba; Argentina. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Centro de Química Aplicada; ArgentinaFil: Ribotta, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Ciencia y Tecnología de Alimentos Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Ciencia y Tecnología de Alimentos Córdoba; ArgentinaFil: Benitez, Elisa Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Química Básica y Aplicada del Nordeste Argentino. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Química Básica y Aplicada del Nordeste Argentino; Argentina. Universidad Tecnológica Nacional. Facultad Regional Resistencia. Departamento de Ingeniería Química. Laboratorio de Química Teórica y Experimental; Argentin

Molecular dynamics simulations of the temperature-induced unfolding of crambin follow the Arrhenius equation

Molecular dynamics simulations have been used extensively to model the folding and unfolding of proteins. The rates of folding and unfolding should follow the Arrhenius equation over a limited range of temperatures. This study shows that molecular dynamic simulations of the unfolding of crambin between 500K and 560K do follow the Arrhenius equation. They also show that while there is a large amount of variation between the simulations the average values for the rate show a very high degree of correlation

Terrestrial water load and groundwater fluctuation in the Bengal Basin

Groundwater-level fluctuations represent hydraulic responses to changes in groundwater storage due to aquifer recharge and drainage as well as to changes in stress that include water mass loading and unloading above the aquifer surface. The latter ‘poroelastic’ response of confined aquifers is a well-established phenomenon which has been demonstrated in diverse hydrogeological environments but is frequently ignored in assessments of groundwater resources. Here we present high-frequency groundwater measurements over a twelve-month period from the tropical, fluvio-deltaic Bengal Aquifer System (BAS), the largest aquifer in south Asia. The groundwater level fluctuations are dominated by the aquifer poroelastic response to changes in terrestrial water loading by processes acting over periods ranging from hours to months; the effects of groundwater flow are subordinate. Our measurements represent the first direct, quantitative identification of loading effects on groundwater levels in the BAS. Our analysis highlights the potential limitations of hydrogeological analyses which ignore loading effects in this environment. We also demonstrate the potential for employing poroelastic responses in the BAS and across other tropical fluvio-deltaic regions as a direct, in-situ measure of changes in terrestrial water storage to complement analyses from the Gravity and Climate Experiment (GRACE) mission but at much higher resolution

Interrogation of an Enzyme Library Reveals the Catalytic Plasticity of Naturally Evolved [4+2] Cyclases

\ua9 2023 The Authors. ChemBioChem published by Wiley-VCH GmbH.Stereoselective carbon-carbon bond forming reactions are quintessential transformations in organic synthesis. One example is the Diels-Alder reaction, a [4+2] cycloaddition between a conjugated diene and a dienophile to form cyclohexenes. The development of biocatalysts for this reaction is paramount for unlocking sustainable routes to a plethora of important molecules. To obtain a comprehensive understanding of naturally evolved [4+2] cyclases, and to identify hitherto uncharacterised biocatalysts for this reaction, we constructed a library comprising forty-five enzymes with reported or predicted [4+2] cycloaddition activity. Thirty-one library members were successfully produced in recombinant form. In vitro assays employing a synthetic substrate incorporating a diene and a dienophile revealed broad-ranging cycloaddition activity amongst these polypeptides. The hypothetical protein Cyc15 was found to catalyse an intramolecular cycloaddition to generate a novel spirotetronate. The crystal structure of this enzyme, along with docking studies, establishes the basis for stereoselectivity in Cyc15, as compared to other spirotetronate cyclases

Astrometric Microlensing with the GAIA satellite

GAIA is the ``super-Hipparcos'' survey satellite selected as a Cornerstone 6 mission by the European Space Agency. GAIA can measure microlensing by the small excursions of the light centroid that occur during events. The all-sky source-averaged astrometric microlensing optical depth is about 10^{-5}. Some 25000 sources will have a significant variation of the centroid shift, together with a closest approach, during the lifetime of the mission. A covariance analysis is used to study the propagation of errors and the estimation of parameters from realistic sampling of the GAIA datastream of transits in the along-scan direction during microlensing events. Monte Carlo simulations are used to study the 2500 events for which the mass can be recovered with an error of less than 50 per cent. These high quality events are dominated by disk lenses within a few tens of parsecs and source stars within a few hundred parsecs. We show that the local mass function can be recovered from the high quality sample to good accuracy. GAIA is the first instrument with the capabilities of measuring the mass locally in very faint objects like black holes and very cool white and brown dwarfs. For only 5 per cent of all astrometric events will GAIA record even one photometric datapoint. There is a need for a dedicated telescope that densely samples the Galactic Centre and spiral arms, as this can improve the accuracy of parameter estimation by a factor of about 10.Comment: 18 pages, 18 figures, MNRAS, in pres

Systematic theoretical study of the spin and orbital magnetic moments of 4d and 5d interfaces with Fe films

Results of ab initio calculations using the relativistic Local Spin Density theory are presented for the magnetic moments of periodic 5d and 4d transition metal interfaces with bcc Fe(001). In this systematic study we calculated the layer-resolved spin and orbital magnetic moments over the entire series. For the Fe/W(001) system, the Fe spin moment is reduced whilst its orbital moment is strongly enhanced. In the W layers a spin moment is induced, which is antiparallel to that of Fe in the first and fourth W layers but parallel to Fe in the second and third W layers. The W orbital moment does not follow the spin moment. It is aligned antiparallel to Fe in the first two W layers and changes sign in the third and fourth W layers. Therefore, Hund's third rule is violated in the first and third W layers, but not in the second and fourth W layers. The trend in the spin and orbital moments over the 4d and 5d series for multilayers is quite similar to previous impurity calculations. These observations strongly suggest that these effects can be seen as a consequence of the hybridization between 5d (4d) and Fe which is mostly due to band filling, and to a lesser extent geometrical effects of either single impurity or interface