Entropic Barrier Research Articles

Generalized Sinkhorn Iterations for Regularizing Inverse Problems Using Optimal Mass Transport

The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be formulated as a linear programming problem, it is in many cases intractable for large problems due to the vast number of variables. A recent development to address this builds on an approximation with an entropic barrier term and solves the resulting optimization problem using Sinkhorn iterations. In this work we extend this methodology to a class of inverse problems. In particular we show that Sinkhorn-type iterations can be used to compute the proximal operator of the transport problem for large problems. A splitting framework is then used to solve inverse problems where the optimal mass transport cost is used for incorporating a priori information. We illustrate the method on problems in computerized tomography. In particular we consider a limited-angle computerized tomography problem, where a priori information is used to compensate for missing measurements.

The concept of entropic rectifier facing experiments.

The transport of molecules in confined media is subject to entropic barriers. So theoretically, asymmetry of the confinement length may lead to molecular ratchets with entropy as the only driving force for the biased transport. We address experimentally this question by performing alternative ionic current measurements on electrolytes confined in neutral conical nanopores. In case anions and cations widely differ in size, we show that rectification of ionic current can be obtained that depends on ions size and cycle frequency, consistently with the entropic ratchet mechanism.

Out-of-equilibrium dynamics and extended textures of topological defects in spin ice

We study the interplay of topological bottlenecks and energetic barriers to equilibration in a Coulomb spin liquid where a short-range energetic coupling between defects charged under an emergent gauge field supplements their entropic long-range Coulomb interaction. This work is motivated by the prevalence of memory effects observed across a wide range of geometrically frustrated magnetic materials, possibly including the spontaneous Hall effect observed in Pr2Ir2O7. Our model is canonical spin-ice model on the pyrochlore lattice, where farther-neighbour spin couplings give rise to a nearest-neighbor interaction between topological defects which can easily be chosen to be unnatural or not, i.e. attractive or repulsive between defects of equal gauge charge. Among the novel features of this model are the following. After applying a field quench, a rich dynamical approach to equilibrium emerges, dominated by multi-scale energy barriers responsible for long-lived magnetization plateaux. These even allow for the metastability of a "fragmented" spin liquid, an elusive regime where partial order co-exists with a spin liquid. Perhaps most strikingly, the attraction produces clusters of defects whose stability is due to a combination of energetic barriers for their break-up and proximity of opposite charges along with an entropic barrier generated by the topological requirement of annihilating a defect only together with an oppositely charged counterpart. These clusters may take the form of a "jellyfish" spin texture, comprising an arrangement of same-sign gauge-charges, centered on a hexagonal ring with branches of arbitrary length. The ring carries a clockwise or counterclockwise circular flow of magnetisation. This emergent toroidal degrees of freedom provides a possibility for time reversal symmetry breaking with possible relevance to the spontaneous Hall effect observed in Pr2Ir2O7.

Diffusion of Aromatics in Silicalite-1: Experimental and Theoretical Evidence of Entropic Barriers

A specific computational methodology based on transition state theory (Kolokathis, P. D. et al. Mol. Simul., 2014, 40, 80–100) is evolved and applied for calculation of the self-diffusion coefficients of p-xylene and benzene in silicalite-1 at infinite dilution. In addition, we study the orientational distributions of phenyl rings and methyl stems of p-xylene and benzene sorbed in the zeolite and check for the existence of entropic barriers to translational motion. A new reduction method for the states appearing in the free energy profiles is presented and used for calculation of transition rate constants for elementary jumps. Quasi-elastic neutron scattering measurements are also conducted and compared with the simulation results. A major conclusion from both experiments and simulations is that p-xylene diffuses roughly 100 times faster than benzene when sorbed at low occupancy in silicalite. Benzene encounters strong entropic barriers to translational motion at channel intersections, where it can adopt ...

Cooperative Self-Assembly of a Quaternary Complex Formed by Two Cucurbit[7]uril Hosts, Cyclobis(paraquat-p-phenylene), and a "Designer" Guest.

The self-assembly in aqueous solution of the well-known cyclophane, cyclobis(paraquat-p-phenylene) (BB(4+) ), and two cucurbit[7]uril (CB7) hosts around a simple hydroquinol-based, diamine guest (GH2 (2+) ) was investigated by (1) H NMR and electronic absorption spectroscopies, electrospray mass spectrometry and DFT computations. The formation of a quaternary supramolecular assembly [GH2 (2+) ⋅BB(4+) ⋅ (CB7)2 ] was shown to be a very efficient process, which takes place not only because of the attractive forces between each of the hosts and the guest, but also because of the lateral interactions between the hosts in the final assembly. This complementary set of attractive interactions results in clear cooperative binding effects that help overcome the entropic barriers for multiple component assembly.

Cooperative Self‐Assembly of a Quaternary Complex Formed by Two Cucurbit[7]uril Hosts, Cyclobis(paraquat‐p‐phenylene), and a “Designer” Guest

AbstractThe self‐assembly in aqueous solution of the well‐known cyclophane, cyclobis(paraquat‐p‐phenylene) (BB4+), and two cucurbit[7]uril (CB7) hosts around a simple hydroquinol‐based, diamine guest (GH22+) was investigated by 1H NMR and electronic absorption spectroscopies, electrospray mass spectrometry and DFT computations. The formation of a quaternary supramolecular assembly [GH22+⋅BB4+⋅ (CB7)2] was shown to be a very efficient process, which takes place not only because of the attractive forces between each of the hosts and the guest, but also because of the lateral interactions between the hosts in the final assembly. This complementary set of attractive interactions results in clear cooperative binding effects that help overcome the entropic barriers for multiple component assembly.

DNA Translocation through Nanopores at Physiological Ionic Strengths Requires Precise Nanoscale Engineering.

Many important processes in biology involve the translocation of a biopolymer through a nanometer-scale pore. Moreover, the electrophoretic transport of DNA across nanopores is under intense investigation for single-molecule DNA sequencing and analysis. Here, we show that the precise patterning of the ClyA biological nanopore with positive charges is crucial to observe the electrophoretic translocation of DNA at physiological ionic strength. Surprisingly, the strongly electronegative 3.3 nm internal constriction of the nanopore did not require modifications. Further, DNA translocation could only be observed from the wide entry of the nanopore. Our results suggest that the engineered positive charges are important to align the DNA in order to overcome the entropic and electrostatic barriers for DNA translocation through the narrow constriction. Finally, the dependencies of nucleic acid translocations on the Debye length of the solution are consistent with a physical model where the capture of double-stranded DNA is diffusion-limited while the capture of single-stranded DNA is reaction-limited.

Effect of intrinsic curvature and edge tension on the stability of binary mixed-membrane three-junctions.

We use a combination of coarse-grained molecular dynamics simulations and theoretical modeling to examine three-junctions in mixed lipid bilayer membranes. These junctions are localized defect lines in which three bilayers merge in such a way that each bilayer shares one monolayer with one of the other two bilayers. The resulting local morphology is non-lamellar, resembling the threefold symmetric defect lines in inverse hexagonal phases, but it regularly occurs during membrane fission and fusion events. We realize a system of junctions by setting up a honeycomb lattice, which in its primitive cell contains two hexagons and four three-line junctions, permitting us to study their stability as well as their line tension. We specifically consider the effects of lipid composition and intrinsic curvature in binary mixtures, which contain a fraction of negatively curved lipids in a curvature-neutral background phase. Three-junction stability results from a competition between the junction and an open edge, which arises if one of the three bilayers detaches from the other two. We show that the stable phase is the one with the lower defect line tension. The strong and opposite monolayer curvatures present in junctions and edges enhance the mole fraction of negatively curved lipids in junctions and deplete it in edges. This lipid sorting affects the two line tensions and in turn the relative stability of the two phases. It also leads to a subtle entropic barrier for the transition between junction and edge that is absent in uniform membranes.

Current and efficiency optimization under oscillating forces in entropic barriers**Project supported by the Istanbul University, Turkey (Grant No. 55383).

The transport of externally overdriven particles confined in entropic barriers is investigated under various types of oscillating and temporal forces. Temperature, load, and amplitude dependence of the particle current and energy conversion efficiency are investigated in three dimensions. For oscillating forces, the optimized temperature–load, amplitude–temperature, and amplitude–load intervals are determined when fixing the amplitude, load, and temperature, respectively. By using three-dimensional plots rather than two-dimensional ones, it is clearly shown that oscillating forces provide more efficiency compared with a temporal one in specified optimized parameter regions. Furthermore, the dependency of efficiency to the angle between the unbiased driving force and a constant force is investigated and an asymmetric angular dependence is found for all types of forces. Finally, it is shown that oscillating forces with a high amplitude and under a moderate load lead to higher efficiencies than a temporal force at both low and high temperatures for the entire range of contact angle.

Unusually Facile Thermal Homodienyl-[1,5]-Hydrogen Shift Reactions in Photochemically Generated Vinyl Aziridines.

A range of photochemically generated tri- and tetracyclic vinyl aziridines have been found to undergo a general and surprisingly low temperature ring opening through a [1,5]-hydrogen shift reaction. The rate of the process was found to be highly dependent on the structure and substitution around the azirdine ring and the alkene terminus, with some substrates being observed to undergo ring opening at temperatures as low as 25 °C. The rigid nature of these polycyclic systems precludes a conformational explanation of these rate differences, and an Eyring study confirmed a negligible entropic barrier to the reaction. However, the Eyring plots for two different aziridines systems showed a significant difference in their enthalpies of activation. It is therefore believed that the levels of aziridine ring strain, as well as electronic effects, are the dominant factors in this sequence.

Pseudo-one-dimensional nucleation in dilute polymer solutions.

Pathogenic protein fibrils have been shown in vitro to have nucleation-dependent kinetics despite the fact that one-dimensional structures do not have the size-dependent surface energy responsible for the lag time in classical theory. We present a theory showing that the conformational entropy of the peptide chains creates a free-energy barrier that is analogous to the translational entropy barrier in higher dimensions. We find that the dynamics of polymer rearrangement make it very unlikely for nucleation to succeed along the lowest free-energy trajectory, meaning that most of the nucleation flux avoids the free-energy saddle point. We use these results to construct a three-dimensional model for amyloid nucleation that accounts for conformational entropy, backbone H bonds, and side-chain interactions to compute nucleation rates as a function of concentration.

Energy barriers, entropy barriers, and non-Arrhenius behavior in a minimal glassy model.

We study glassy dynamics using a simulation of three soft Brownian particles confined to a two-dimensional circular region. If the circular region is large, the disks freely rearrange, but rearrangements are rarer for smaller system sizes. We directly measure a one-dimensional free-energy landscape characterizing the dynamics. This landscape has two local minima corresponding to the two distinct disk configurations, separated by a free-energy barrier that governs the rearrangement rate. We study several different interaction potentials and demonstrate that the free-energy barrier is composed of a potential-energy barrier and an entropic barrier. The heights of both of these barriers depend on temperature and system size, demonstrating how non-Arrhenius behavior can arise close to the glass transition.

Research of Particle Transport with External Driving Force and Entropy Barrier

Transport of Brownian particle moving along a three-dimensional throat-like channel is investigated in the presence of an external constant force. The solution of the Fick–Jacobs equation in the situation is solved, and the probability current density and particle current describing the motion of particle are obtained. It is found that entropy barrier and external force can reverse the direction of particle current. The motion of Brownian particle can be tuned by the entropy barrier and the external force.

Temperature-Dependent Suppression of Polymer Diffusion in Polymer Nanocomposites.

The polymer center-of-mass tracer diffusion coefficient in athermal polymer nanocomposites (PNCs) composed of polystyrene and phenyl-capped, spherical silica nanoparticles was measured over a range of temperatures and nanoparticle concentrations using elastic recoil detection. The polymer tracer diffusion coefficient in the PNC relative to the bulk decreases with increasing nanoparticle concentration and is unexpectedly more strongly reduced at higher temperatures. This unusual temperature dependence of polymer diffusion in PNCs cannot be explained by the reptation model or a modified version incorporating an effective tube diameter. Instead we show that our results are consistent with a mechanism based on nanoparticle-imposed configurational entropy barriers.

Theoretical model of biomacromolecule through nanopore including effects of electrolyte and excluded volume

A theoretical model for the translocation process of biomacromolecule is developed based on the self-consistent field theory (SCFT), where the biomacromolecule is regarded as a self-avoiding polymer chain actuated by the external potential. In this theoretical model, the external potential, the Coulomb electrostatic potential of the charged ions (the electrolyte effect), and the attractive interaction between the polymer and the nanopore (the excluded volume effect) are all considered, which have effects on the free energy landscape and conformation entropy during the translocation stage. The result shows that the entropy barrier of the polymer in the solution with high valence electrolyte is much larger than that with low valence electrolyte under the same condition, leading to that the translocation time of the DNA molecules in the solution increases when the valence electrolyte increases. In addition, the attractive interaction between the polymer and the nanopore increases the free energy of the polymer, which means that the probability of the translocation through the nanopore increases. The average translocation time decreases when the excluded volume effect parameter increases. The electrolyte effect can prolong the average translocation time. The simulation results agree well with the available experimental results.

An intrinsically disordered entropic switch determines allostery in Phd-Doc regulation.

Conditional cooperativity is a common mechanism involved in transcriptional regulation of prokaryotic type II toxin-antitoxin operons and is intricately related to bacterial persistence. It allows the toxin component of a toxin-antitoxin module to act as a co-repressor at low doses of toxin as compared to antitoxin. When toxin level exceeds a certain threshold, however, the toxin becomes a de-repressor. Most antitoxins contain an intrinsically disordered region (IDR) that typically is involved in toxin neutralization and repressor complex formation. To address how the antitoxin IDR is involved in transcription regulation, we studied the phd-doc operon from bacteriophage P1. We provide evidence that the IDR of Phd provides an entropic barrier precluding full operon repression in the absence of Doc. Binding of Doc results in a cooperativity switch and consequent strong operon repression, enabling context-specific modulation of the regulatory process. Variations of this theme are likely to be a common mechanism in the autoregulation of bacterial operons that involve intrinsically disordered regions.

Monte Carlo simulations of vector pseudospins for strains: Microstructures and martensitic conversion times

We present systematic temperature-quench Monte Carlo simulations on discrete-strain pseudospin model Hamiltonians to study microstructural evolutions in ferroelastic transitions with two-component vector order parameters (NOP=2) in 2-spatial dimensions. The zero value pseudospin is the single high-temperature phase while the low-temperature phase has Nv variants. Thus the number of nonzero values of pseudospin are triangle-to-centered rectangle (Nv=3), square-to-oblique (Nv=4) and triangle-to-oblique (Nv=6). The model Hamiltonians contain a transition-specific Landau energy term, a domain wall cost or Ginzburg term, and power-law anisotropic interaction potential, induced from a strain compatibility condition. On quenching below a transition temperature, we find behaviour similar to the previously studied square-to-rectangle transition (NOP=1,Nv=2), showing that the rich behaviour found, is generic. Thus we find for two-component order parameters that the same Hamiltonian can describe both athermal and isothermal martensite regimes for different material parameters. The athermal/isothermal/austenite parameter regimes and temperature–time–transformation diagrams are understood, as previously, through parametrization of effective-droplet energies. In the athermal regime, we find rapid conversions below a spinodal-like temperature and austenite-martensite conversion delays above it, as in the experiment. The delays show early incubation behaviour, and at the transition to austenite the delay times have Vogel–Fulcher divergences and are insensitive to Hamiltonian energy scales, suggesting that entropy barriers are dominant. Systematic temperature quench experiments can look for martensite formation and growth during conversion-incubations, divergences, and distributions close to the transition.

Extinction of oscillating populations.

Established populations often exhibit oscillations in their sizes that, in the deterministic theory, correspond to a limit cycle in the space of population sizes. If a population is isolated, the intrinsic stochasticity of elemental processes can ultimately bring it to extinction. Here we study extinction of oscillating populations in a stochastic version of the Rosenzweig-MacArthur predator-prey model. To this end we develop a WKB (Wentzel, Kramers and Brillouin) approximation to the master equation, employing the characteristic population size as the large parameter. Similar WKB theories have been developed previously in the context of population extinction from an attracting multipopulation fixed point. We evaluate the extinction rates and find the most probable paths to extinction from the limit cycle by applying Floquet theory to the dynamics of an effective four-dimensional WKB Hamiltonian. We show that the entropic barriers to extinction change in a nonanalytic way as the system passes through the Hopf bifurcation. We also study the subleading pre-exponential factors of the WKB approximation.

Harnessing atomistic simulations to predict the rate at which dislocations overcome obstacles

Predicting the rate at which dislocations overcome obstacles is key to understanding the microscopic features that govern the plastic flow of modern alloys. In this spirit, the current manuscript examines the rate at which an edge dislocation overcomes an obstacle in aluminum. Predictions were made using different popular variants of Harmonic Transition State Theory (HTST) and compared to those of direct Molecular Dynamics (MD) simulations. The HTST predictions were found to be grossly inaccurate due to the large entropy barrier associated with the dislocation–obstacle interaction. Considering the importance of finite temperature effects, the utility of the Finite Temperature String (FTS) method was then explored. While this approach was found capable of identifying a prominent reaction tube, it was not capable of computing the free energy profile along the tube. Lastly, the utility of the Transition Interface Sampling (TIS) approach was explored, which does not need a free energy profile and is known to be less reliant on the choice of reaction coordinate. The TIS approach was found capable of accurately predicting the rate, relative to direct MD simulations. This finding was utilized to examine the temperature and load dependence of the dislocation–obstacle interaction in a simple periodic cell configuration. An attractive rate prediction approach combining TST and simple continuum models is identified, and the strain rate sensitivity of individual dislocation obstacle interactions is predicted.

Separation of diamondoids in crude oils using molecular sieving techniques to allow compound-specific isotope analysis

Correlation of condensates with other condensates or oils has been a long standing problem due to the significantly depleted abundance of biomarkers in condensates. On the contrary, diamondoids are thermally stable and are present in relatively high abundance in highly mature oils and condensates. Hence, stable carbon isotope measurements of individual diamondoids using compound specific isotope analysis (CSIA) can potentially assist in solving this correlation problem (He, M., Moldowan, J.M., Nemchenko-Rovenskaya, A., Peters, K.E., 2012. Oil families and their inferred source rocks in the Barents Sea and northern Timan-Pechora Basin, Russia. American Association of Petroleum Geologists Bulletin 96, 1121–1146). However, CSIA analysis requires well resolved diamondoid concentrates, a daunting task due to the low concentration of diamondoids relative to non-diamondoids in oils and even condensates generated from carbonates and coals. The diamondoids co-elute substantially with the abundant iso- and cycloalkanes in gas chromatography (GC) chromatograms of oils. Here, isolation of adamantane and its methylated derivatives was achieved by way of concurrent desorption and adsorption processes in a column with two segments. The top segment contained 60Å pore silica gel powder with a pre-adsorbed hydrocarbon fraction containing the diamondoid mixture. The bottom segment was filled with a microporous adsorbent – a form of a commercial zeolite, β CP814 E∗, heated at 550°C for 13h under open air conditions to give a uniform pore size of ca. 9.5Å. With the larger micropore size (9.5Å) than the molecular dimensions of adamantane (7.4Å), molecular sieving to exclude diamondoids through the microporous adsorbent segment is induced by an entropy barrier arising from the mismatch between the bulky shape of diamondoid molecules and the elliptical shape of pore entrance in this adsorbent. It was also found that the separation was sensitive to operating temperature. The impact of pore size and shape of the microporous adsorbent on the quality of the diamondoid separation is addressed, as well as diamondoid abundance in the original hydrocarbon fraction.