We investigate the effects of structural periodicity on wave localization in one-dimensional periodic-on-average disordered systems and derive two relations from the properties of the spectral periodicity and symmetry of the underlying periodic systems. These two relations predict equal localization lengths between disordered systems with different randomness. Comparisons with numerically simulated results show good agreement. These relations are used to explain some properties of the frequency dependence of the localization length, such as oscillation, asymmetry, etc.

The current investigation probes frustration that arises in a Blume-Emery-Griffiths system due to competing biquadratic $\left(\pm K\right)$ interactions while uniform bilinear and crystal-field interactions are maintained. This competition directly affects the clustering and density of nonmagnetic impurities. All calculations have been conducted using a hierarchical lattice in conjunction with renormalization-group methods. Phase diagrams have been calculated for a series of planes of constant biquadratic coupling while varying the temperature and concentration of annealed vacancies in the system. Each phase diagram reveals three qualitatively unique basins of attraction, each sharing renormalization-group trajectories that flow to common sinks.

We evaluate the energy dissipation rate of an optically driven Brownian particle in a polymer solution utilizing the generalized version of Harada and Sasa’s equality [Phys. Rev. Lett. 95, 130602 (2005)] by Deutsch and Narayan [Phys. Rev. E 74, 026112 (2006)]. The irreversible work of a small system is estimated from readily obtainable quantities. By adopting the time-dependent memory function obtained by microrheology measurement, directly obtained works are in excellent agreement with those calculated from the generalized fluctuation dissipation theorem for nonequilibrium steady states. This result implies that the colloidal particle in a polymer solution can be described by the generalized Langevin equation.

For crystalline materials, the microscopic origin of plasticity is well understood in terms of the dynamics of topological defects. For amorphous materials, the underlying structural disorder prevents such a description. Therefore identifying and characterizing the microscopic plastic events in amorphous materials remains an important challenge. We show direct evidence for the coexistence of reversible and irreversible plastic events (T1 events) at the microscopic scale in both experiments and simulations of two-dimensional foam. In the simulations, we also demonstrate a link between the reversibility of T1 events and pathways in the potential energy landscape of the system.

Understanding and controlling polymorph selection is important because the structure of a crystal is critical to its properties. We have explored polymorph selection during nucleation in the hard-core repulsive Yukawa fluid. This model has two polymorphs (bcc and fcc), the relative stability of which can be adjusted by changing the potential parameters. We used seeded molecular-dynamics simulations to follow the evolution of the metastable bcc structure in the fcc stable region. It was found that the degree of undercooling affected the development of the bcc seeds. At small undercoolings, the bcc seed became a bcc crystal, but at large undercoolings bcc seeds became fcc crystals. Homogenously nucleated simulations were also compared to colloidal experiments. The simulations yielded nuclei of similar shape to the experimentally observed nuclei and a similar minimum size of growth. The simulated nuclei had more bcc signature than the experimental nuclei, but upon further growth the bcc signature faded, indicating that the difference between simulations and experiments may be due to the experimental nuclei having more time to resolve their structure.

Maximal- and minimal-height distributions (MAHD, MIHD) of two-dimensional interfaces grown with the nonlinear equations of Kardar-Parisi-Zhang (KPZ, second order) and of Villain-Lai-Das Sarma (VLDS, fourth order) are shown to be different. Two universal curves may be MAHD or MIHD of each class depending on the sign of the relevant nonlinear term, which is confirmed by results of several lattice models in the KPZ and VLDS classes. The difference between MAHD and MIDH is connected with the asymmetry of the local height distribution. A simple, exactly solvable deposition-erosion model is introduced to illustrate this feature. The average extremal heights scale with the same exponent of the average roughness. In contrast to other correlated systems, generalized Gumbel distributions do not fit those MAHD and MIHD, nor those of Edwards-Wilkinson growth.

Laser manipulation of trapped radial $4^{\prime }$-n-pentyl-4-cyanobiphenyl (5CB) nematic liquid-crystal droplets induced by molecular reordering is presented. We show experimentally that optical tweezers having linear, elliptical, or circular polarization can break the radial symmetry of the initial molecular organization inside a radial nematic droplet. Static distorted or twisted deformation modes and steady or unsteady nonlinear rotational dynamics are observed. Statics results are analyzed in terms of light-induced radial or left-right symmetry breaking effects associated with optical reorientation. The dynamical observations are compared with simulations from a slab analog model, for which orientational processes driven by optical nonlinearities can be accurately described. This study confirms that light-induced bulk reordering is an essential ingredient towards the understanding of the behavior of radial nematic liquid-crystal droplets in laser tweezers, as suggested by previous studies.

Many factors influence the shapes of living and manufactured membranes. In addition to boundary conditions, surface tension, and curvature, the ordering of particles embedded in or attached to a membrane can strongly influence its equilibrium shape. As a simple model of such ordering, we consider rodlike particles that align to form a so-called nematic phase in the plane of the membrane. We call any sheet with such embedded orientational order a nematic membrane. Nematic membranes can occur in biological cells, liquid crystal films, manufactured materials, and other soft matter systems. By formulating the free energy of nematic films using tensor contractions from differential geometry, we elucidate the elastic terms allowed by symmetry, and indicate differences from hexatic membranes. We find that topological defects in the orientation field can cause the membrane to buckle over a size set by the competition between surface tension and in-plane elasticity. In the absence of bending rigidity the resulting shape is universal, known as a parabolic pseudosphere or a revolved tractrix. This buckling is the two-dimensional analog of the bent cores of line defects that are frequently observed in bulk nematic liquid crystals. Bending costs oppose such buckling and modify the shape in a predictable manner. In particular, the anisotropic rigidities of nematic membranes lead to different shapes for aster and vortex defects, in principle enabling measurement of couplings specific to nematic membranes.

Synperonic F-108 (generic name, “pluronic”) is a micelle forming triblock copolymer of type $ABA$, where $A$ is polyethylene oxide (PEO) and $B$ is polypropylene oxide (PPO). At high temperatures, the hydrophobicity of the PPO chains increase, and the pluronic molecules, when dissolved in an aqueous medium, self-associate into spherical micelles with dense PPO cores and hydrated PEO coronas. At appropriately high concentrations, these micelles arrange in a face centered cubic lattice to show inverse crystallization, with the samples exhibiting high-temperature crystalline and low-temperature fluidlike phases. By studying the evolution of the elastic and viscous moduli as temperature is increased at a fixed rate, we construct the concentration-temperature phase diagram of Synperonic F-108. For a certain range of temperatures and at appropriate sample concentrations, we observe a predominantly elastic response. Oscillatory strain amplitude sweep measurements on these samples show pronounced peaks in the loss moduli, a typical feature of soft solids. The soft solidlike nature of these materials is further demonstrated by measuring their frequency-dependent mechanical moduli. The storage moduli are significantly larger than the loss moduli and are almost independent of the applied angular frequency. Finally, we perform strain rate frequency superposition experiments to measure the slow relaxation dynamics of this soft solid.

Using a continuum bead-spring Monte Carlo model, we study the anomalous diffusion dynamics of a self-avoiding tethered membrane by means of extensive computer simulations. We focus on the subdiffusive stochastic motion of the membrane’s central node in the regime of flat membranes at temperatures above the membrane folding transition. While at times, larger than the characteristic membrane relaxation time ${\tau }_R$, the mean-square displacement of the center of mass of the sheet, $⟨R_c^2⟩$, as well as that of its central node, $⟨R_n^2⟩$, show the normal Rouse diffusive behavior with a diffusion coefficient $D_N$ scaling as $D_N\propto N^{-1}$ with respect to the number of segments $N$ in the membrane, for short times $t\le {\tau }_R$ we observe a multiscale dynamics of the central node, $⟨R_n^2⟩\propto t^{\alpha }$, where the anomalous diffusion exponent $\alpha$ changes from $\alpha \approx 0.86$ to $\approx 0.27$, and then to $\alpha \approx 0.5$, before diffusion turns eventually to normal. By means of simple scaling arguments we show that our main result, $\alpha \approx 0.27$, can be related to particular mechanisms of membrane dynamics which involve different groups of segments in the membrane sheet. A comparative study involving also linear polymers demonstrates that the diffusion coefficient of self-avoiding tethered membranes, containing $N$ segments, is three times smaller than that of linear polymer chains with the same number of segments.

We predict various detectable mechanical responses to the presence of local DNA defects which are defined as short DNA segments exhibiting mechanical properties obviously different from the 50 nm persistence length based semiflexible polymer model. The defects discussed are kinks and flexible hinges either permanently fixed on DNA or thermally excited. Their effects on extension shift, the effective persistence length, the end-to-end distance distribution, and the cyclization probability are computed using a transfer-matrix method. Our predictions will be useful in future experimental designs to study DNA nicks or mismatch base pairs, mechanics of specific DNA sequences, and specific DNA-protein interaction using magnetic tweezer, fluorescence resonance energy transfer, plasmon resonance techniques, and the traditional biochemistry cyclization probability measurements.

The capacity of transcription factors to activate gene expression is encoded in the promoter sequences, which are composed of short regulatory motifs that function as transcription factor binding sites (TFBSs) for specific proteins. To the best of our knowledge, the structural property of TFBSs that controls transcription is still poorly understood. Rigidity is one of the important structural properties of DNA, and plays an important role in guiding DNA-binding proteins to the target sites efficiently. After analyzing the rigidity of 2897 TFBSs in 1871 human promoters, we show that TFBSs are generally more flexible than other genomic regions such as exons, introns, $3^{\prime }$ untranslated regions, and TFBS-poor promoter regions. Furthermore, we find that the density of TFBSs is consistent with the average rigidity profile of human promoters upstream of the transcription start site, which implies that TFBSs directly influence the promoter structure. We also examine the local rigid regions probably caused by specific TFBSs such as the DNA sequence TATA(A/T)A(A/T) box, which may inhibit nucleosomes and thereby facilitate the access of transcription factors bound nearby. Our results suggest that the structural property of TFBSs accounts for the promoter structure as well as promoter activity.

We study scarring phenomena in open quantum systems. We show numerical evidence that individual resonance eigenstates of an open quantum system present localization around unstable short periodic orbits in a similar way as their closed counterparts. The structure of eigenfunctions around these classical objects is not destroyed by the opening. This is exposed in a paradigmatic system of quantum chaos, the cat map.

We present a global payoff-based strategy updating model for studying cooperative behavior of a networked population. We adopt the Prisoner’s Dilemma game and the snowdrift game as paradigms for characterizing the interactions among individuals. We investigate the model on regular, small-world, and scale-free networks, and find multistable cooperation states depending on the initial cooperator density. In particular for the snowdrift game on small-world and scale-free networks, there exist a discontinuous phase transition and hysteresis loops of cooperator density. We explain the observed properties by theoretical predictions and simulation results of the average number of neighbors of cooperators and defectors, respectively. Our work indicates that individuals with more neighbors have a trend to preserve their initial strategies, which has strong impacts on the strategy updating of individuals with fewer neighbors; while the fact that individuals with few neighbors have to become cooperators to avoid gaining the lowest payoff plays significant roles in maintaining and spreading of cooperation strategy.

Using computational modeling, we introduce patches of self-oscillating gels undergoing the Belousov-Zhabotinsky (BZ) reaction into a nonreactive polymer network and thereby demonstrate how these BZ gels can be harnessed to impart remarkable functionality to the entire system. By first focusing on two adjacent patches of BZ gels, we show that the patches’ oscillations can become synchronized in phase or out of phase, with the oscillation frequency depending on the synchronization mode and the spatial separation between these domains. We then apply these results to an array of five adjacent BZ patches and by varying the distance between these pieces, we dramatically alter the dynamical behavior of the patterned gel. For example, the sample can be made to exhibit a unidirectional traveling wave or display a concerted expansion and contraction, properties that are valuable for creating gel-based devices, such as micropumps and microactuators. The findings point to a “modular” design approach, which can impart different functionality simply by arranging identical pieces of BZ gels into distinct spatial arrangements within a polymer matrix.

A clustered network is characterized by a number of distinct sparsely linked subnetworks (clusters), each with dense internal connections. Such networks are relevant to biological, social, and certain technological networked systems. For a clustered network the occurrence of global synchronization, in which nodes from different clusters are synchronized, is of interest. We consider Kuramoto-type dynamics and obtain an analytic formula relating the critical coupling strength required for global synchronization to the probabilities of intracluster and intercluster connections, and provide numerical verification. Our work also provides direct support for a previous spectral-analysis-based result concerning the role of random intercluster links in enhancing the synchronizability of a clustered network.

The dispersion equation is analyzed for waves in a strongly magnetized, electron-positron plasma in which counterstreaming electrons are cold in their respective rest frames. For propagation parallel to the magnetic field the dispersion equation factorizes into equations for two longitudinal modes and four transverse modes. Instabilities occur in both longitudinal and transverse modes, with the most notable being at low wave numbers where a longitudinal branch has purely imaginary frequency. For oblique propagation at small angles, the modes reconnect at points where the parallel modes intersect, either deviating away from each another, or being separated by a pair of complex modes. In addition, intrinsically oblique branches of the dispersion equation appear. The results are applied to an oscillating model for a pulsar magnetosphere, in which the oscillations are purely temporal with a frequency well below relevant wave frequencies, and in which the counterstreaming becomes highly relativistic. We assume that the medium may be treated as time stationary in treating the wave dispersion and wave growth. The wave properties, including the wave frequency, vary periodically with the phase of the oscillations. The fastest growing instability is when the counterstreaming is nonrelativistic or mildly relativistic. A given wave can experience bursts of growth over many oscillations. Mode coupling associated with the cyclotron resonance may be effective in generating the observed orthogonally polarized modes at phases of the oscillation where the (relativistic) cyclotron and wave frequencies are comparable.

The Weibel instability in the quantum plasma case is treated by means of a fluidlike (moments) approach. Quantum modifications to the macroscopic equations are then identified as effects of the first or second kind. Quantum effects of the first kind correspond to a dispersive term, similar to the Bohm potential in the quantum hydrodynamic equations for plasmas. Effects of the second kind are due to the Fermi statistics of the charge carriers and can become the dominant influence for strong degeneracy. The macroscopic dispersion relations are of higher order than those for the classical Weibel instability. This corresponds to the presence of a cutoff wave number even for the strong temperature anisotropy case.

We propose a scheme to generate single-cycle powerful terahertz (THz) pulses by ultrashort intense laser pulses obliquely incident on an underdense plasma slab of a few THz wavelengths in thickness. THz waves are radiated from a transient net current driven by the laser ponderomotive force in the plasma slab. Analysis and particle-in-cell simulations show that such a THz source is capable of providing power of megawatts to gigawatts, field strength of MV/cm–GV/cm, and broad tunability range, which is potentially useful for nonlinear and high-field THz science and applications.

Necessary and sufficient conditions for the stability of a sleeping top described by dynamic equations of six state variables, Euler equations, and Poisson equations, by a two-degree-of-freedom system, Krylov equations, and by a one-degree-of-freedom system, nutation angle equation, is obtained by the Lyapunov direct method, Ge-Liu second instability theorem, an instability theorem, and a Ge-Yao-Chen partial region stability theorem without using the first approximation theory altogether.