Pedestrian flows in bounded domains with obstacles

In this paper, we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon-positive measures generated by a push-forward recursive relation. We assume that two fundamental aspects of pedestrian behavior rule the dynamics of the system: on the one hand, the will to reach specific targets, which determines the main direction of motion of the walkers; on the other hand, the tendency to avoid crowding, which introduces interactions among the individuals. The resulting model is able to reproduce several experimental evidences of pedestrian flows pointed out in the specialized literature, being at the same time much easier to handle, from both the analytical and the numerical point of view, than other models relying on nonlinear hyperbolic conservation laws. This makes it suitable to address two-dimensional applications of practical interest, chiefly the motion of pedestrians in complex domains scattered with obstacles.      

Highly Hydrophilic Copolymers of N,N‐Dimethylacrylamide,Acrylamido‐2‐methylpropanesulfonic acid,and Ethylenedimethacrylate: Nanoscale Morphology in the Swollen State and Use as Exotemplates for Synthesis of Nanostructured Ferric Oxide

The polymer framework of water‐swollen copolymers of N,N‐dimethylacrylamide, acrylamido‐2‐methylpropanesulfonic acid, and ethylenedimethacrylate (nominal cross‐linking degrees of 4, 8, and 20 mol %) is composed of highly expanded domains, with “pores” not less than 6 nm in diameter. When the 4 % cross‐linked copolymer (DAE 26‐4) is swollen with a 10^?4 M solution of 4‐hydroxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl (TEMPOL) in water, MeOH, EtOH, or nBuOH, the molecules of the paramagnetic probe rotate rapidly (τ<1000 ps) and as fast as in the bulk liquid in the case of water. The swelling degree of DAE 26‐4 is related to the Hansen solubility parameters of a number of liquids, including linear alcohols up to n‐octanol. It is also found that the rotational correlation time of TEMPOL in the copolymer swollen by water and the lightest alcohols increases with decreasing specific absorbed volume. Time‐domain NMR spectrometry of water‐swollen DAE 26‐4 shows that sorption of only 14 % of the liquid required for its complete swelling is enough for full hydration of the polymer chains. Accordingly, in fully swollen DAE 26‐4 the longitudinal relaxation time of water closely approaches the value of pure water. {¹³C} CP‐MAS NMR on partially and fully water swollen samples of DAE 26‐4 shows that swelling increases the mobility of the polymer chains, as clearly indicated by the narrowing of the best‐resolved peaks. DAE 26‐4 was used as an exotemplate for the synthesis of nanocomposites composed of the polymer and nanostructured Fe₂O₃ through a series of ion‐exchange/precipitation cycles. After the first cycle the nanoparticles are 3–4 nm in diameter, with practically unchanged size after subsequent cycles (up to five). In fact, the nanoparticle size never exceeded the diameter of the largest available pores. This suggests that the polymer framework controls the growth of the nanoparticles according to the template‐controlled synthesis scheme. Selected‐area electron diffraction, TEM, and high‐resolution electron microscopy show that the nanostructured inorganic phase is composed of hematite.     

Community repeated interaction and strategic delegation

A large population of fixed-type agents engage in exclusive pairwise relationships in a decentralized setting. At the onset, agents randomly meet in pairs under private information of individual time-invariant types. They play a voluntary contribution game. At the end of the first period, members of each pair either stay together in the second period, in which case reported information is common knowledge, or quit and meet randomly new partners, under private information of individual types. Thus, either long-term or short-term relationships may arise. We show that there are values of the parameters such that information extracted in the first period has a positive effect on social efficiency. We give an interpretation of our results in terms of advantageous delegation of decisions to uninformed agents. Finally, we consider several extensions of the model in which our results still hold.     

Spatio-Temporal Organization in a Morphochemical Electrodeposition Model: Analysis and Numerical Simulation of Spiral Waves

In this paper we derive Hopf instability conditions for the morphochemical mathematical model for alloy electrodeposition introduced and experimentally validated in Bozzini et al. (J. Solid State Electrochem., 17:467–479, 2013). Using normal form theory we show that in the neighborhood of the Hopf bifurcation, essential features of the system dynamics are captured by a specific Complex Ginzburg-Landau Equation (CGLE). The derived CGLE yields analytical results on the existence and stability of spiral waves. Moreover, the arising of spiral instability is discussed in terms of the relevant system parameters and the related phenomenology is investigated numerically. To face with the numerical approximation of the spiral structures and of their longtime oscillating behavior we apply an Alternating Direction Implicit (ADI) method based on high order finite differences in space.     

Simultaneous diastereo- and enantioseparation of farnesoid X receptor (FXR) agonists with a quinine carbamate-based chiral stationary phase

In the frame of a project aimed at finding non-steroidal farnesoid X receptor (FXR) agonists, we identified 4-(2,4-dimethoxyphenyl)-3,6-dimethyl-1-(2-tolyl)-4,8-dihydro-1H-pyrazole[3,4-e][1,4]thiazepin-7-one (1) as a hit endowed with FXR activity. Most of the compounds synthesised during the hit-to-lead optimisation work were characterised by the presence of two chiral centres and were therefore obtained as mixtures of anti(±)- and syn(±)-diastereoisomers. A restricted sub-set of species harboured with a carboxylic acid group on the distal phenyl ring of the biphenyl (a(±)5 (A1) and s(±)5 (S1)) or the phenoxyphenyl (a(±)6 (A2) and s(±)6 (S2)) moiety at C-4 position of the pyrazole[3,4-e][1,4]thiazepin-7-one core, resulted in suitable diastereo- and enantioresolution with a quinine (QN) carbamate-derived chiral stationary phase (CSP). Differently from the compounds usually analysed with QN-based CSPs, the couples A1/S1 and A2/S2 were atypical selectands, in which the two chiral carbon atoms reside at a remote position with respect to the carboxylic function, the main “point of attack” to the CSP. We produced evidence that the scarcely employed normal-phase (NP) eluent systems represent the elective choice for achieving the simultaneous diastereo- and enantioseparation of this class of compounds over the usually preferred reversed-phase (RP) and polar-organic (PO) modes of elution. Indeed, after the optimisation of the eluent composition, NP conditions allowed to obtain profitable enantioselectivity profiles, along with excellent diastereoselectivity levels (α(A1)?=?1.07, R _S(A1)?=?1.15; α(S1)?=?1.09, R _S(S1)?=?1.47; α(A2)?=?1.08, R _S(A2)?=?1.31; and α(S2)?=?1.06, R _S(S2)?=?1.18). The optimised NP methods are suitable for simultaneously providing information on the diastereo- and enantiopurity of the investigated compounds.

Ketoprofen enantioseparation with a Cinchona alkaloid based stationary phase: Enantiorecognition mechanism and release studies

With the present contribution, we demonstrate that the baseline separation of ketoprofen enantiomers can be successfully achieved (α = 1.09; R_S = 1.60) in the reversed‐phase mode of elution with a commercially available anion‐exchange‐based chiral stationary phase, incorporating the quinine 2,6‐diisopropylphenyl carbamate derivative as the enantioresolving unit. Focused modification of the eluent composition indicated a stereoselective role of hydrophobic and π–π interactions between the selector and selectand units, besides the prime ionic intermolecular interaction. The mechanistic hypotheses based on the chromatographic data were confirmed by in silico molecular dynamic simulations, which allowed us to establish the network of selector–selectand interactions underlying the stereorecognition process at a molecular level. The validated method was successfully used to evaluate the drug content and release profile of ketoprofen‐loaded polymeric film, showing drug homogeneous distribution into the film and no preferential interactions between the polymer and one of the enantiomers, with the racemate released at each time point.     

A Non-Maxwellian Steady Distribution for One-Dimensional Granular Media

We consider a nonlinear Fokker–Planck equation for a one-dimensional granular medium. This is a kinetic approximation of a system of nearly elastic particles in a thermal bath. We prove that homogeneous solutions tend asymptotically in time toward a unique non-Maxwellian stationary distribution.     

Organometallic complexes with biological molecules. I. Diorganotin(IV)chloro protoporphyrin IX complexes: Solid-state and solution-phase characterization

Protoporphyrin IX (H₄PPIX) complexes of diorganotin(IV)chloro moieties with formula (R₂SnCl)₂H₂PPIX (R?Me, Bu and Ph) have been obtained and their solid-state and solution-phase configurations have been studied through spectroscopic investigations. Coordination of the side-chain carboxylates of H₄PPIX to R₂Sn(IV)Cl moieties, with bridging carboxylate (COO^?) has been inferred by comparison of the free and coordinated H₄PPIX IR spectra, while the occurrence of a five-coordinated tin(IV) atom in a cis-R₂ trigonal bipyramidal structure has been deduced, for all of the synthesized complexes, by rationalization of the nuclear quadrupole splitting parameters, according to the point-charge model formalism. Fanally, the solution-phase spectral features of (R₂SnCl)₂^?H₂PPIX are in agreement with the monomeric character of the protoporphyrin IX, under the experimental conditions used.