Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations

We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite time blow-up and as well as global existence of solutions of the problem.Comment: 11 pages. Minor changes and added reference

The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations

In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the Camassa-Holm equation over a long time scale. This general class of nonlocal wave equations model bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. To justify the Camassa-Holm approximation we show that approximation errors remain small over a long time interval. To be more precise, we obtain error estimates in terms of two independent, small, positive parameters $\epsilon$ and $\delta$ measuring the effect of nonlinearity and dispersion, respectively. We further show that similar conclusions are also valid for the lower order approximations: the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.Comment: 24 pages, to appear in Discrete and Continuous Dynamical System

Guidance on Stimulus Materials

PACHELBEL WP4 “Stimulus Materials” uses findings from WP3 (Policy Assumptions) and from additional sources to prepare stimulus materials for the group-based process “STAVE” implemented in WP5. The output was material to inform and stimulate the group-based process. The material was of two types: a set of questionnaires common to all partners (EVOC/CAPA/SIMI questionnaires), and material that is issue-specific and individually produced for each country. EVOC/CAPA/SIMI short questionnaires serve as a comparative tool between countries, giving insight on the social construction of “sustainable consumption” across the PACHELBEL population. Partners asked participants to fill out the set individually at the first meeting of the STAVE group, results were then analyzed and data were fed back for discussion by group participants at their second meeting. A “re-test” was then conducted at the third of three group meetings. The present report details the representations revealed through this methodology – but moreover the impact of applying such a technique in STAVE groups in France, Germany, Romania, Spain, Sweden and the UK (where the methodology was slightly altered). The issue-and-country-specific material consists of an informative simulated newspaper article on the particular issue addressed in a given STAVE process, and/or other materials (for example, humorous drawings). The report details how this material was developed, and the experience of applying these stimulus materials in each country. On this basis, guidance for future STAVE processes is offered. Foremost among observations is that PACHELBEL stimulus materials serve a purpose that is distinct from that of “group exercises” as developed in WP5. The materials contributing to the formation of a group identity, a reflexive group norm, and a shared information basis. As such, stimulus materials prepare the group for a cooperative investigative process

Light and pH-induced Changes in Structure and Accessibility of Transmembrane Helix B and Its Immediate Environment in Channelrhodopsin-2

A variant of the cation channel channelrhodopsin-2 from Chlamydomonas reinhardtii (CrChR2) was selectively labeled at position Cys-79 at the end of the first cytoplasmic loop and the beginning of transmembrane helix B with the fluorescent dye fluorescein (acetamidofluorescein). We utilized (i) time- resolved fluorescence anisotropy experiments to monitor the structural dynamics at the cytoplasmic surface close to the inner gate in the dark and after illumination in the open channel state and (ii) time-resolved fluorescence quenching experiments to observe the solvent accessibility of helix B at pH 6.0 and 7.4. The light-induced increase in final anisotropy for acetamidofluorescein bound to the channel variant with a prolonged conducting state clearly shows that the formation of the open channel state is associated with a large conformational change at the cytoplasmic surface, consistent with an outward tilt of helix B. Furthermore, results from solute accessibility studies of the cytoplasmic end of helix B suggest a pH-dependent structural heterogeneity that appears below pH 7. At pH 7.4 conformational homogeneity was observed, whereas at pH 6.0 two protein fractions exist, including one in which residue 79 is buried. This inaccessible fraction amounts to 66% in nanodiscs and 82% in micelles. Knowledge about pH-dependent structural heterogeneity may be important for CrChR2 applications in optogenetics

A simulation-guided fluorescence correlation spectroscopy tool to investigate the protonation dynamics of cytochrome c oxidase

Fluorescence correlation spectroscopy (FCS) is a single molecule based technique to temporally resolve rate-dependent processes by correlating the fluorescence fluctuations of individual molecules traversing through a confocal volume. In addition, chemical processes like protonation or intersystem crossing can be monitored in the sub-microsecond range. FCS thereby provides an excellent tool for investigations of protonation dynamics in proton pumps like cytochrome c oxidase (CcO). To achieve this, the pH- dependent fluorescent dye fluorescein was attached as a protonation probe to the CcO surface via site-specific labeling of single reactive cysteines that are located close to the entry point of a proton input channel (K-pathway). The analysis of protonation dynamics is complicated by overlapping triplet and protonation rates of the fluorophore. A Monte Carlo simulation based algorithm was developed to facilitate discrimination of these temporally overlapping processes thus allowing for improved protonation reaction rate determination. Using this simulation-guided approach we determined precise local proton association and dissociation rates and provide information about protein surface effects, such as proton collecting antennae, on the transport properties of proton transfer channels

Inverse folding for antibody sequence design using deep learning

We consider the problem of antibody sequence design given 3D structural information. Building on previous work, we propose a fine-tuned inverse folding model that is specifically optimised for antibody structures and outperforms generic protein models on sequence recovery and structure robustness when applied on antibodies, with notable improvement on the hypervariable CDR-H3 loop. We study the canonical conformations of complementarity-determining regions and find improved encoding of these loops into known clusters. Finally, we consider the applications of our model to drug discovery and binder design and evaluate the quality of proposed sequences using physics-based methods.Comment: 2023 ICML Workshop on Computational Biology, model weights available at https://zenodo.org/record/816469

Finding the Right Blend: Interplay Between Structure and Sodium Ion Conductivity in the System Na5AlS4-Na4SiS4

The rational design of high performance sodium solid electrolytes is one of the key challenges in modern battery research. In this work, we identify new sodium ion conductors in the substitution series Na(5-x)Al(1-x)Si(x)S4 (0 <= x <= 1), which are entirely based on earth-abundant elements. These compounds exhibit conductivities ranging from 1.64 center dot 10(-7) for Na4SiS4 to 2.04 center dot 10(-5) for Na-8.5(AlS4)(0.5)(SiS4)(1.5) (x = 0.75). We determined the crystal structures of the Na+-ion conductors Na4SiS4 as well as hitherto unknown Na5AlS4 and Na-9(AlS4)(SiS4). Na+-ion conduction pathways were calculated by bond valence energy landscape (BVEL) calculations for all new structures highlighting the influence of the local coordination symmetry of sodium ions on the energy landscape within this family. Our findings show that the interplay of charge carrier concentration and low site symmetry of sodium ions can enhance the conductivity by several orders of magnitude

Variable depth KDV equations and generalizations to more nonlinear regimes

We study here the water-waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known, that for such regimes, a generalization of the KdV equation (somehow linked to the Camassa-Holm equation) can be derived and justified by A. Constantin, D. Lannes "The hydrodynamical relevance of the Camassa-Holm and Degasperis-Processi equations" when the bottom is flat. We generalize here this result with a new class of equations taking into account variable bottom topographies. Of course, the many variable depth KdV equations existing in the literature are recovered as particular cases. Various regimes for the topography regimes are investigated and we prove consistency of these models, as well as a full justification for some of them. We also study the problem of wave breaking for our new variable depth and highly nonlinear generalizations of the KDV equations

A sample of radio-loud QSOs at redshift ~ 4

We obtained spectra of 60 red, starlike objects (E< 18.8) identified with FIRST radio sources, S_{1.4GHz} > 1 mJy. Eight are QSOs with redshift z> 3.6.Combined with our pilot search (Benn et al 2002), our sample of 121 candidates yields a total of 18 z > 3.6 QSOs (10 of these with z > 4.0). 8% of candidates with S_{1.4GHz} 10 mJy are QSOs with z > 3.6. The surface density of E 1mJy, z> 4 QSOs is 0.003 deg^{-2}. This is currently the only well-defined sample of radio-loud QSOs at z ~ 4 selected independently of radio spectral index. The QSOs are highly luminous in the optical (8 have M_B < -28, q_0 = 0.5, H_0 = 50 kms^{-1}Mpc^{-1}). The SEDs are as varied as those seen in optical searches for high-redshift QSOs, but the fraction of objects with weak (strongly self-absorbed) Ly alpha emission is marginally higher (3 out of 18) than for high-redshift QSOs from SDSS (5 out of 96).Comment: Accepted for publication in MNRAS, 9 pages, Latex, 5 postscript figures, 1 landscape table (postscript