Random Dimer Research Articles

Double-Dimer Pairings and Skew Young Diagrams

We study the number of tilings of skew Young diagrams by ribbon tiles shaped like Dyck paths, in which the tiles are "vertically decreasing". We use these quantities to compute pairing probabilities in the double-dimer model: Given a planar bipartite graph $G$ with special vertices, called nodes, on the outer face, the double-dimer model is formed by the superposition of a uniformly random dimer configuration (perfect matching) of $G$ together with a random dimer configuration of the graph formed from $G$ by deleting the nodes. The double-dimer configuration consists of loops, doubled edges, and chains that start and end at the boundary nodes. We are interested in how the chains connect the nodes. An interesting special case is when the graph is $\varepsilon(\mathbb Z\times\mathbb N)$ and the nodes are at evenly spaced locations on the boundary $\mathbb R$ as the grid spacing $\varepsilon\to0$.

Transport properties of a ladder with two random dimer chains

We investigate the transport properties of a ladder with two random dimer (RD) chains. It is found that there are two extended states in the ladder with identical RD chains and a critical state regarded as an extended state in the ladder with pairing RD chains. Such a critical state is caused by the chiral symmetry. The ladder with identical RD chains can be decoupled into two isolated RD chains and the ladder with pairing RD chains can not. The analytic expressions of the extended states are presented for the ladder with identical RD chains.

Nature of the enhanced resonant modes in one-dimensional photonic random dimer systems

The propagation of light in a one-dimensional multilayer stack is examined for a disordered system with short range correlation. As known in the random dimer model, pairing the defect elements at random breaks down the Anderson localization and opens a frequency window of extended propagating modes around the predicted conventional dimer resonance. By dealing with host and defect layers with identical phase thicknesses at both host and defect principal standing resonances, we demonstrate the existence of a new ballistic-like regime at an additional standing commuting resonance. Moreover, by suitably tuning the host standing and conventional defect dimer resonances relative to each other, the transmission responses are both turned into a ballistic transmission regime. By scaling the transmission coefficient over the system length within the resonance window, we analyse the nature of the propagating modes, i.e. ballistic or diffusive. Beyond the resonance, quantitative views on the different transmission regimes and their related phase transitions are examined, pointing out the possibility of designing attractive ballistic resonant optical devices with adjustable transmission responses.

Lipids Enhance Apolipoprotein C-II-Derived Amyloidogenic Peptide Oligomerization but Inhibit Fibril Formation

We investigated the effect of submicellar lipids on amyloid fibril formation. Thioflavin T fluorescence studies showed that submicellar levels of the short-chain phospholipids, dipentanoylphosphatidylcholine and dihexanoylphosphatidylcholine, strongly inhibited amyloid fibril formation by an 11-residue peptide derived from human apolipoprotein C-II (apoC-II(60-70)). In contrast, sedimentation equilibrium analysis of these peptide-lipid mixtures indicated the presence of soluble oligomeric complexes. To acquire insight into the atomic level influences of these lipids on the initial stages of aggregation of the peptide, we performed molecular dynamics (MD) simulations coupled with umbrella sampling to determine dimerization free energies of a number of beta-stranded and random coil dimer complexes, both in the presence and absence of lipids. The simulations indicate that, in contrast to their inhibitory effects on fibril formation, short-chain phospholipids promote the formation and stabilization of dimers by enhancing intersubunit hydrophobic interactions. On the basis of these experimental and computational results, we propose that peptide-bound lipids can inhibit amyloid fibril formation by trapping of dimers and other oligomeric species in diverse nonfibril forming conformations, reducing their likelihood of acquiring subunit conformations prone to fibril nucleation and growth. In light of the demonstrated cytotoxicity of amyloid peptide oligomers, our results suggest that, by enhancing the stability of oligomeric peptide species, the presence of solvated lipids may contribute to the cytotoxicity of fibrillogenic proteins and peptides.

Localization properties of acoustic waves in the random-dimer media

Propagation of acoustic waves in the one-dimensional (1D) random-dimer (RD) medium is studied by three distinct methods. First, using the transfer-matrix method, we calculate numerically the localization length $\ensuremath{\xi}$ of acoustic waves in a binary chain (one in which the elastic constants take on one of two values). We show that when there exists short-range correlation in the medium---which corresponds to the RD model---the localization-delocalization transition occurs at a resonance frequency ${\ensuremath{\omega}}_{c}$. The divergence of $\ensuremath{\xi}$ near ${\ensuremath{\omega}}_{c}$ is studied, and the critical exponents that characterize the power-law behavior of $\ensuremath{\xi}$ near ${\ensuremath{\omega}}_{c}$ are estimated for the regimes $\ensuremath{\omega}g{\ensuremath{\omega}}_{c}$ and $\ensuremath{\omega}l{\ensuremath{\omega}}_{c}$. Second, an exact analytical analysis is carried out for the delocalization properties of the waves in the RD media. In particular, we predict the resonance frequency at which the waves can propagate in the entire chain. Finally, we develop a dynamical method, based on the direct numerical simulation of the governing equation for propagation of the waves, and study the nature of the waves that propagate in the chain. It is shown that only the resonance frequency can propagate through the 1D media. The results obtained with all the three methods are in agreement with each other.

The ballistic resonance of transversal mechanical waves in random-dimer systems

The propagation of transversal mechanical waves in one-dimensional disordered system is studied in presence of the short-range correlation. The dimer and host unit cells are constructed within a particular way that provides perfect unity transmission resonances over all of the system length. Moreover, while dealing with the on-site correlation this interesting configuration also supplies the ballistic vibration propagating modes for any amount of the mass disorder in opposition with the well-known conventional diffusive random dimer model. This process is appropriate to design better mechanical filters with very high adjustable ballistic transmission quality.

Scaling laws for the transmission of random binary dielectric multilayered structures

We investigate several scaling aspects of the transmission spectrum of disordered one-dimensional dielectric structures. We consider a binary stratified medium composed of a random sequence of $N$ slabs with refraction indices satisfying the Bragg condition. The mode for which the optical thickness corresponds to half wavelength is insensitive to disorder and fully transparent. The average transmission in a frequency range around this resonance decays as $1∕{N}^{1∕2}$, and the localization length diverges quadratically as this resonance mode is approached. In the vicinity of the quarter-wavelength mode, the localization length diverges logarithmically and the frequency averaged transmission exhibits an stretched exponential dependence on the total thickness. At the quarter-wavelength resonance, the Lyapunov exponent for different realizations of disorder has a Gaussian distribution leading to distinct scaling laws for the geometric and arithmetic averages of the transmission. The scaling laws for the half- and quarter-wavelength modes are analogous to those found in electronic one-dimensional Anderson models with random dimers and pure off-diagonal disorder, respectively, which are known to display similar violations of the usual exponential Anderson localization.

Relation between directed polymers in random media and random-bond dimer models

We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the hexagonal lattice. For the latter, we demonstrate the equivalence of the canonical ensemble for the dimer model and the grand-canonical description for polymers by performing explicitly the continuum limit. Using this equivalence for the random bond dimer model on a square lattice, we resolve a previously observed discrepancy between numerical results for the random dimer model and a replica approach for polymers in random media. Further potential applications of the equivalence are briefly discussed.

Lyapunov exponents for unitary Anderson models

We study a unitary version of the one-dimensional Anderson model, given by a five diagonal deterministic unitary operator multiplicatively perturbed by a random phase matrix. We fully characterize positivity and vanishing of the Lyapunov exponent for this model throughout the spectrum and for arbitrary distributions of the random phases. This includes Bernoulli distributions, where in certain cases a finite number of critical spectral values, with vanishing Lyapunov exponent, exist. We establish similar results for a unitary version of the random dimer model.

Off-rate and concentration diversity in multidonor-derived dimers of immunoglobulin G

IgG-dimers in multidonor-derived preparations of IgG antibodies represent not only agents of therapeutic potential, but also molecules of basic immunological interest since their composition mirrors the currently unknown range of clonal concentrations and affinities. To analyze this fundamental type of diversity, a computational model is developed in agreement with a density functional theory and used to simulate the dissociation kinetics of dimers separated from a 5000 donor-derived IgG preparation (protein concentration: 0.74mg/mL) via superimposition of 8100 arbitrary combinations of off-rates and initial concentrations. The Greedy algorithm-like procedure described requires iterative and consecutive changes of 8 from a total of 11 fitting parameters and allows to approximate the probability density distributions of either quantities within defined limits (apparent off-rates: ∼4×10−4 to 9×10−17s−1; concentrations: ∼3×10−20 to 1×10−11M) by lognormal distributions of log–log10-type, each of them adapted with four particular parameters, as well as the number of different dimer populations (∼2×1013). Moreover, reasonably dimensioned equilibrium constants involved in monovalent and bivalent random IgG dimerization are estimated by using a mean on-rate of 2.5×105M−1s−1 and interrelationships of molecular parameters derived from known models for antibody–antigen interaction.

Effect of nonlinear interactions on resonant states of the random dimer model

A simple Kronig–Penney model for 1D mesoscopic systems withδ peak potentials is used to study numerically the effect of non-linear interaction on the resonantstates of the random dimer model. It is shown that the nonlinear interaction increases or decreasesthe width of the resonances depending on both its sign and strength. The resonance widthΔE is a power law decaying with the system size asL−γ. Theexponent γ decreases linearly with the nonlinear interaction strength when the dimer impurityconcentration increases. The resonance energy states, in these systems, are shifteddepending on the kind of interaction. Further investigations are provided on the effect ofnonlinearity on conductance fluctuations near the resonances.

Ac-field-controlled localization-delocalization transition in a one-dimensional disordered system

Based on the random dimer model, we study correlated disorder in a one-dimensional system driven by a strong ac field. As the correlations in a random system may generate extended states and enhance transport in dc fields, we explore the role that ac fields have on these properties. We find that similar to ordered structures, ac fields renormalize the effective hopping constant to a smaller value and thus help to localize a state. We find that ac fields control then a localization-delocalization transition in a given one-dimensional system with correlated disorder. The competition between band renormalization (band collapse and dynamic localization), Anderson localization, and the structure correlation is shown to result in interesting transport properties.

Effect of electron interactions on the electronic properties of random dimer systems

We have studied the electronic wave propagation through a one-dimensional random dimer system in the presence of non-linear interactions. By investigating the scaling dependence of the extended states bandwidth, the non-linear interaction is found to improve the electronic conduction in such systems. It is also found that the resonance energy states in these systems are shifted depending on the kind of interaction. Further investigations are provided on the localization transition around these resonances.

Quantized Berry Phases as a Local Order Parameter of a Quantum Liquid

We propose to use quantized Berry phases as local order parameters of gapped quantum liquids, which are invariant under some anti-unitary operation. After presenting a general prescription, the scheme is applied for Heisenberg models with frustrations and two dimensional extended Su-Schrieffer-Heeger models associated with a random dimer covering. In each phases, the quantized Berry phases, as 0 or $\pi$, describe the ground state texture pattern of local singlet bonds and dimer bonds. Also possible applications to large classes of correlated electron systems are discussed.

Fullerene C 60 as stabiliser for acrylic polymers

The influence of fullerene C 60 additives on thermal behaviour and thermodegradation of poly- n-alkyl acrylates, from butyl to heptyl, and of corresponding polymethacrylates was investigated by thermogravimetry in dynamical conditions and pyrolysis/gas chromatography in isothermal conditions at 400–650 °C. The fullerene is a well-known efficient acceptor of radicals and its presence influences the thermal degradation of acrylic polymers, shifting the decomposition process from a radical pathway to a non-radical mechanism. For poly- n-alkyl acrylates the addition of fullerene leads to increase in the yields of olefin and alcohol, degradation products coming from non-radical pathways. On the other hand, the yields of the pyrolysis products deriving from the random main-chain scission, i.e. monomer, dimer, saturated diester, trimer, corresponding acetate and methacrylate, decrease. The recorded temperatures of maximum weight loss (obtained by thermogravimetric experiments) are slightly increased by the presence of fullerene. The effect of fullerene is more noticeable in the thermal behaviour of poly- n-alkyl methacrylates, in fact the enhancements of the temperature of maximum weight loss are 19–25 °C. The mixtures containing fullerene give rise to a marked decrease of the monomer yield and, at the same time, an increase of olefin and methacrylic acid amounts. The fullerene acts as radical acceptor suppressing the unzipping process and favouring the non-radical side-chain reactions.

Exotic Versus Conventional Scaling and Universality in a Disordered Bilayer Quantum Heisenberg Antiferromagnet

We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.

Membrane Binding Modulates the Quaternary Structure of CTP:Phosphocholine Cytidylyltransferase

CTP:phosphocholine cytidylyltransferase (CCT), a key enzyme that controls phosphatidylcholine synthesis, is regulated by reversible interactions with membranes containing anionic lipids. Previous work demonstrated that CCT is a homodimer. In this work we show that the structure of the dimer interface is altered upon encountering membranes that activate CCT. Chemical cross-linking reactions were established which captured intradimeric interactions but not random CCT dimer collisions. The efficiency of capturing covalent cross-links with four different reagents was diminished markedly upon presentation of activating anionic lipid vesicles but not zwitterionic vesicles. Experiments were conducted to show that the anionic vesicles did not interfere with the chemistry of the cross-linking reactions and did not sequester available cysteine sites on CCT for reaction with the cysteine-directed cross-linking reagent. Thus, the loss of cross-linking efficiency suggested that contact sites at the dimer interface had increased distance or reduced flexibility upon binding of CCT to membranes. The regions of the enzyme involved in dimerization were mapped using three approaches: 1) limited proteolysis followed by cross-linking of fragments, 2) yeast two-hybrid analysis of interactions between select domains, and 3) disulfide bonding potential of CCTs with individual cysteine to serine substitutions for the seven native cysteines. We found that the N-terminal domain (amino acids 1-72) is an important participant in forming the dimer interface, in addition to the catalytic domain (amino acids 73-236). We mapped the intersubunit disulfide bond to the cystine 37 pair in domain N and showed that this disulfide is sensitive to anionic vesicles, implicating this specific region in the membrane-sensitive dimer interface.

Two types of extended states in random dimer barrier superlattices

We study numerically the effects of short-range correlated disorder on the electronic and transport properties of intentionally disordered GaAs–Al x Ga 1− x As superlattices. We consider layers having identical thickness where the Al concentration x takes at random two different values with the constraint that one of them appears only in pairs, i.e. the random dimer barrier. Various physical quantities such as the conductance, the universal fluctuation conductance, the localization length, the resistance and its probability distribution are statistically computed by means of the transfer matrix formalism to discriminate the nature of the electronic states. In spite of the presence of disorder, the system exhibits two kinds of sets of propagating states lying below the barrier due to the characteristic structure of the superlattice. The states close to the resonance can be viewed as consisting of weakly localized states with very large localization length. In the band tails, i.e. for vanishing conductance, the states are strongly localized. The nature of the transition between these two regimes is quantitatively investigated through relevant physical quantities.

Test of replica theory: Thermodynamics of two-dimensional model systems with quenched disorder

We study the statistics of thermodynamic quantities in two related systems with quenched disorder: A $(1+1)$-dimensional planar lattice of elastic lines in a random potential and the two-dimensional random bond dimer model. The first system is examined by a replica-symmetric Bethe Ansatz (RBA) while the latter is studied numerically by a polynomial algorithm which circumvents slow glassy dynamics. We establish a mapping of the two models which allows for a detailed comparison of RBA predictions and simulations. Over a wide range of disorder strength, the effective lattice stiffness and cumulants of various thermodynamic quantities in both approaches are found to agree excellently. Our comparison provides a detailed quantitative confirmation of the replica approach and renders the planar line lattice a unique testing ground for concepts in random systems.

Localization-delocalization transition in a presence of correlated disorder: The random dimer model

The one dimensional dimer model is investigated and the localization length calculated exactly. The presence of delocalized states at $E_c = \epsilon_{a,b}$ of two possible values of the chemical potential in case of $\mid\epsilon_a-\epsilon_b\mid \leq 2 $ is confirmed and the corresponding indices of the localization length were calculated. The singular integral equation connecting the density of states with the inverse localization length is solved and the analytic expression for the density of states compared with the numerical calculations.