Red Orange and Bitter Orange IntegroPectin: Structure and Main Functional Compounds

DRIFT, HPLC-MS, and SPME-GC/MS analyses were used to unveil the structure and the main functional compounds of red (blood) orange (Citrus sinensis) and bitter orange (Citrus aurantium). The IntegroPectin samples show evidence that these new citrus pectins are comprised of pectin rich in RG-I hairy regions functionalized with citrus biophenols, chiefly flavonoids and volatile molecules, mostly terpenes. Remarkably, IntegroPectin from the peel of fresh bitter oranges is the first high methoxyl citrus pectin extracted via hydrodynamic cavitation, whereas the red orange IntegroPectin is a low methoxyl pectin. C. aurantium IntegroPectin has a uniquely high concentration of adsorbed flavonoids, especially the flavanone glycosides hesperidin, naringin, and eriocitrin.     

A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM

In this paper, we study numerical methods for an optimal control problem with pointwise state constraints. The traditional approaches often need to deal with the deltasingularity in the dual equation, which causes many difficulties in its theoretical analysis and numerical approximation. In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state, whose optimality condition is characterized by a fourth order elliptic variational inequality. Then direct numerical algorithms （nonconforming finite element approximation） are proposed for the inequality, and error estimates of the finite element approximation are derived. Numerical experiments illustrate the effectiveness of the new approach.     

Gel to glass transition in simulation of a valence-limited colloidal system

We numerically study a simple model for thermoreversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures T. By studying a large region of T and packing fraction phi we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered nonergodic state. We find that there are two distinct arrest lines for the system: a glass line at high packing fraction, and a gel line at low phi and T. The former is rather vertical (phi controlled), while the latter is rather horizontal (T controlled) in the phi-T plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on phi, while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in phi along low-T isotherms, seen most strikingly in the behavior of the nonergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics.     

Non-Gaussian energy landscape of a simple model for strong network-forming liquids: Accurate evaluation of the configurational entropy

We present a numerical study of the statistical properties of the potential energy landscape of a simple model for strong network-forming liquids. The model is a system of spherical particles interacting through a square-well potential, with an additional constraint that limits the maximum number of bonds Nmax per particle. Extensive simulations have been carried out as a function of temperature, packing fraction, and Nmax. The dynamics of this model are characterized by Arrhenius temperature dependence of the transport coefficients and by nearly exponential relaxation of dynamic correlators, i.e., features defining strong glass-forming liquids. This model has two important features: (i) Landscape basins can be associated with bonding patterns. (ii) The configurational volume of the basin can be evaluated in a formally exact way, and numerically with an arbitrary precision. These features allow us to evaluate the number of different topologies the bonding pattern can adopt. We find that the number of fully bonded configurations, i.e., configurations in which all particles are bonded to Nmax neighbors, is extensive, suggesting that the configurational entropy of the low temperature fluid is finite. We also evaluate the energy dependence of the configurational entropy close to the fully bonded state and show that it follows a logarithmic functional form, different from the quadratic dependence characterizing fragile liquids. We suggest that the presence of a discrete energy scale, provided by the particle bonds, and the intrinsic degeneracy of fully bonded disordered networks differentiates strong from fragile behavior.     

Molecular correlation functions for uniaxial ellipsoids in the isotropic state

We perform event-driven molecular dynamics simulations of a system composed by uniaxial hard ellipsoids for different values of the aspect ratio and packing fraction. We compare the molecular orientational-dependent structure factors previously calculated within the Percus-Yevick approximation with the numerical results. The agreement between theoretical and numerical results is rather satisfactory. We also show that, for specific orientational quantities, the molecular structure factors are sensitive to the particle shape and can be used to distinguish prolate from oblate ellipsoids. A first order theoretical expansion around the spherical shape and a geometrical analysis of the configurations confirms and explains such an observation.     

Phase diagram of patchy colloids: towards empty liquids

We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbors offers the possibility of generating liquid states (i.e., states with temperature T lower than the liquid-gas critical temperature) with a vanishing occupied packing fraction (phi), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the (T-phi) plane, possibly favoring the establishment of homogeneous disordered materials at small phi, i.e., stable equilibrium gels.     

Dynamics in the presence of attractive patchy interactions

We report extensive Monte Carlo and event-driven molecular dynamics simulations of a liquid composed of particles interacting via hard-sphere interactions complemented by four tetrahedrally coordinated short-range attractive ("sticky") spots, a model introduced several years ago by Kolafa and Nezbeda (Kolafa, J.; Nezbeda, I. Mol. Phys. 1987, 87, 161). To access the dynamic properties of the model, we introduce and implement a new event-driven molecular dynamics algorithm suited to study the evolution of hard bodies interacting, beside the repulsive hard-core, with a short-ranged interpatch square well potential. We evaluate the thermodynamic properties of the model in deep supercooled states, where the bond network is fully developed, providing evidence of density anomalies. Different from models of spherically symmetric interacting particles, the liquid can be supercooled without encountering the gas-liquid spinodal in a wide region of packing fractions phi. Around an optimal phi, a stable fully connected tetrahedral network of bonds develops. By analyzing the dynamics of the model we find evidence of anomalous behavior: around the optimal packing, dynamics accelerate on both increasing and decreasing phi. We locate the shape of the isodiffusivity lines in the (phi - T) plane and establish the shape of the dynamic arrest line in the phase diagram of the model. Results are discussed in connection with colloidal dispersions of sticky particles and gel-forming proteins and their ability to form dynamically arrested states.     

Model for reversible colloidal gelation

We report a numerical study, covering a wide range of packing fraction Phi and temperature T, for a system of particles interacting via a square well potential supplemented by an additional constraint on the maximum number n(max) of bonded interactions. We show that, when n(max)<6, the liquid-gas coexistence region shrinks, giving access to regions of low Phi where dynamics can be followed down to low T without an intervening phase separation. We characterize these arrested states at low densities (gel states) in terms of structure and dynamical slowing down, pointing out features which are very different from the standard glassy states observed at high Phi values.     

Relation between the high density phase and the very-high density phase of amorphous solid water

It has been suggested that high-density amorphous (HDA) ice is a structurally arrested form of high-density liquid (HDL) water, while low-density amorphous ice is a structurally arrested form of low-density liquid (LDL) water. Recent experiments and simulations have been interpreted to support the possibility of a second distinct high-density structural state, named very high-density amorphous (VHDA) ice, questioning the LDL-HDL hypothesis. We test this interpretation using extensive computer simulations and find that VHDA is a more stable form of HDA and that, in fact, VHDA should be considered as the amorphous ice of the quenched HDL.