On classical electrodynamics of point particles and mass renormalization: Some preliminary results

Apparently, no rigorous results exist for the dynamics of a classical point particle interacting with the electromagnetic field, as described by the standard Maxwell-Lorentz equations. Some results are given here for the corresponding linearized system (dipole approximation) in the presence of a mechanical linear restoring force. We consider a regularization of the system (Pauli-Fierz model), and explicitly solve the Cauchy problem in terms of normal modes. Then we study the limit of the particle's motion as the regularization is removed. We prove that the particle's motion corresponding to smooth initial data for the field has a well-defined limit if mass is renormalized, while the motion is trivial (i.e. the particle does not move at all) if mass is not renormalized. Moreover, the limit particle's motion corresponding to an interesting class of initial data satifies exactly the Abraham-Lorentz-Dirac equation. Finally, for generic initial data the limit motion is runaway.     

A branch and bound algorithm for scheduling trains in a railway network

The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be re-computed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits.     

Stretching of polymers in isotropic turbulence: a statistical closure

We present a new closure for the mean rate of stretching of a dissolved polymer by homogeneous isotropic turbulence. The polymer is modeled by a bead-spring-type model (e.g., Oldroyd B, FENE-P, Giesekus) and the analytical closure is obtained assuming the Lagrangian velocity gradient can be modeled as a Gaussian, white-noise stochastic process. The resulting closure for the mean stretching depends upon the ratio of the correlation time for strain and rotation. Additionally, we derived a second-order expression for circumstances when strain and rotation have a finite correlation time. Finally, the base level closure is shown to reproduce results from direct numerical simulations by simply modifying the coefficients.     

Cocrystal Formation through Mechanochemistry: from Neat and Liquid‐Assisted Grinding to Polymer‐Assisted Grinding

Mechanochemistry is an effective method for the preparation of multicomponent crystal systems. In the present work, we propose an alternative to the established liquid‐assisted grinding (LAG) approach. Polymer‐assisted grinding (POLAG) is demonstrated to provide a new class of catalysts for improving reaction rate and increasing product diversity during mechanochemical cocrystallization reactions. We demonstrate that POLAG provides advantages comparable to the conventional liquid‐assisted process, whilst eliminating the risk of unwanted solvate formation as well as enabling control of resulting particle size. It represents a new approach for the development of functional materials through mechanochemistry, and possibly opens new routes toward the understanding of the mechanisms and pathways of mechanochemical cocrystal formation.     

Identification of Structure–Activity Relationships from Screening a Structurally Compact DNA‐Encoded Chemical Library

Methods for the rapid and inexpensive discovery of hit compounds are essential for pharmaceutical research and DNA‐encoded chemical libraries represent promising tools for this purpose. We here report on the design and synthesis of DAL‐100K, a DNA‐encoded chemical library containing 103 200 structurally compact compounds. Affinity screening experiments and DNA‐sequencing analysis provided ligands with nanomolar affinities to several proteins, including prostate‐specific membrane antigen and tankyrase 1. Correlations of sequence counts with binding affinities and potencies of enzyme inhibition were observed and enabled the identification of structural features critical for activity. These results indicate that libraries of this type represent a useful source of small‐molecule binders for target proteins of pharmaceutical interest and information on structural features important for binding.     

Temperature effect on the structure and formation kinetics of vinyltriethoxysilane-derived organic/silica hybrids

The structure and formation kinetics of organic/silica hybrid species prepared from acid hydrolysis of vinyltriethoxisilane has been studied in situ by small-angle X-ray scattering (SAXS) at 298, 318, and 333 K in a strongly basic step of the process. The evolution of the SAXS intensity is compatible with the formation of linear chains which grow, coil, and branch to form polymeric macromolecules in solution. The SAXS data were analyzed by the scattering from a persistent chain model for polymeric macromolecules in solution using a modified branching Sharp and Bloomfield global function, which incorporates a branching probability typical of randomly and nonrandomly branched polycondensates, and in a particular case, it is also valid for polydisperse coils of linear chains. Growth of linear chains and coiling dominate the process up to the formation of likely monodisperse Gaussian coils or polydisperse coils of linear chains. The link probability to form a branching point is increased with time to form nonrandomly branched polycondensates in solution. The kinetics of the process is accelerated with temperature, but all the curves formed by the time evolution of the structural parameters in all temperatures can correspondingly be matched on a unique curve by using an appropriate time scaling factor. The activation energy of the process was evaluated as ΔE = 21 ± 1 kJ/mol. The characteristics of the kinetics are in favor of a complex overall mechanism controlled by both condensation reactions and dynamical forces driven by interfacial energy up to the final structure development of the hybrids.     

Bi-functionalization of silica spheres with sulfonic and carboxylic groups via a co-condensation route

Silica spheres with uniform size of 230–250 nm were functionalized with sulfonic groups and bi-functionalized with carboxylic and sulfonic groups via a co-condensation route, by adding the organosilanes (3-(triethoxysilyl)mercaptopropyl and 4-(triethoxysilyl)butyronitrile) to a pre-hydrolized TEOS solution. The conversion of mercapto and cyano groups to, respectively, sulfonic and carboxylic groups was carried out by treating both the samples with nitric acid solution. The presence of alkyl-SO₃H and alkyl-COOH species at the silica surface in an approximate molar ratio of 1:1 was assessed by TG and NMR. FT-IR spectroscopy showed that both Brønsted acidic groups are accessible and give proton-transfer reaction to ammonia with the formation of ammonium ion. Sulfonic groups react irreversibly with ammonia at room temperature at variance with carboxylic groups which give a reversible proton-transfer, in agreement with the stronger Brønsted acidity of the former.