Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength e \varepsilon and the globule size N _G is observed. We find two distinct dynamical regimes: a liquid-like regime (for e \varepsilon < e_s \varepsilon_{{\rm s}}^{} with fast internal dynamics and a solid-like regime (for e \varepsilon > e_s \varepsilon_{{\rm s}}^{} with slow internal dynamics. The cohesion strength e_s \varepsilon_{{\rm s}}^{} of this freezing transition depends on N _G . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with e \varepsilon and scales extensive in N _G . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.     

Phase diagram for the Grover algorithm with static imperfections

We study effects of static inter-qubit interactions on the stability of the Grover quantum search algorithm. Our numerical and analytical results show existence of regular and chaotic phases depending on the imperfection strength e\varepsilon . The critical border e_c\varepsilon_c between two phases drops polynomially with the number of qubits n _q as e_c ~ n_q^-3/2\varepsilon_c \sim n_q^{-3/2} . In the regular phase (e < e_c)(\varepsilon < \varepsilon_c) the algorithm remains robust against imperfections showing the efficiency gain e_c / e\varepsilon_c / \varepsilon for e >~2^-n_q/2\varepsilon \gtrsim 2^{-n_q/2} . In the chaotic phase $(\varepsilon > \varepsilon_c)$(\varepsilon > \varepsilon_c) the algorithm is completely destroyed.     

Adaptive Sub-sampling for Parametric Estimation of Gaussian Diffusions

We consider a Gaussian diffusion X _t (Ornstein-Uhlenbeck process) with drift coefficient γ and diffusion coefficient σ ², and an approximating process Y^e_tY^{\varepsilon}_{t} converging to X _t in L ₂ as ε→0. We study estimators [^(g)]_e\hat{\gamma}_{\varepsilon}, [^(s)]²_e\hat{\sigma}^{2}_{\varepsilon} which are asymptotically equivalent to the Maximum likelihood estimators of γ and σ ², respectively. We assume that the estimators are based on the available N=N(ε) observations extracted by sub-sampling only from the approximating process Y^e_tY^{\varepsilon}_{t} with time step Δ=Δ(ε). We characterize all such adaptive sub-sampling schemes for which [^(g)]_e\hat{\gamma}_{\varepsilon}, [^(s)]²_e\hat{\sigma}^{2}_{\varepsilon} are consistent and asymptotically efficient estimators of γ and σ ² as ε→0. The favorable adaptive sub-sampling schemes are identified by the conditions ε→0, Δ→0, (Δ/ε)→∞, and NΔ→∞, which implies that we sample from the process Y^e_tY^{\varepsilon}_{t} with a vanishing but coarse time step Δ(ε)≫ε. This study highlights the necessity to sub-sample at adequate rates when the observations are not generated by the underlying stochastic model whose parameters are being estimated. The adequate sub-sampling rates we identify seem to retain their validity in much wider contexts such as the additive triad application we briefly outline.     

The conductivity of a 2D system with a doubly periodic arrangement of circular inclusions

We present a scheme for the evaluation of the conductivity and other effective properties of a model composite with a regular anisotropic structure, namely, a 2D system with circular inclusions forming a rectangular array. Exact expressions for the electric potential and the effective conductivity tensor [^(s)] _e\hat \sigma _e were obtained in the form of infinite series. For small inclusion densities, a virial expansion for [^(s)] _e\hat \sigma _e was derived from the general formulas and its applicability conditions were found. The first terms of this expansion yield the well-known Rayleigh result for the isotropic model (square array).     

Magnetooptic effects in antiferromagnetic chromium

Transverse and polar Kerr effects and quadratic magnetooptical effect in reflected light have been discovered and studied in antiferromagnetic chromium. Measurements have been performed in IR, visible, and UV ranges of spectrum in a magnetic field H = 10 kOe. The frequency dispersion of the off-diagonal component of the dielectric constant tensor $\hat \varepsilon $ of chromium has been determined for the first time. An analysis of the magnetooptical data obtained is carried out on the basis of available data on the electronic structure of chromium.     

Defect structures in nematic liquid crystals around charged particles

We numerically study the orientation deformations in nematic liquid crystals around charged particles. We set up a Ginzburg-Landau theory with inhomogeneous electric field. If the dielectric anisotropy e₁ \varepsilon_{1}^{} is positive, Saturn-ring defects are formed around the particles. For e₁ \varepsilon_{1}^{} < 0 , novel “ansa” defects appear, which are disclination lines with their ends on the particle surface. We find unique defect structures around two charged particles. To lower the free energy, oppositely charged particle pairs tend to be aligned in the parallel direction for e₁ \varepsilon_{1}^{} > 0 and in the perpendicular plane for e₁ \varepsilon_{1}^{} < 0 with respect to the background director. For identically charged pairs the preferred directions for e₁ \varepsilon_{1}^{} > 0 and e₁ \varepsilon_{1}^{} < 0 are exchanged. We also examine competition between the charge-induced anchoring and the short-range anchoring. If the short-range anchoring is sufficiently strong, it can be effective in the vicinity of the surface, while the director orientation is governed by the long-range electrostatic interaction far from the surface.     

Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions

We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε ⁻²|log ε|⁻¹ where Ω is the rotational velocity and the coupling parameter is written as ε ⁻² with ε≪1. Three critical speeds can be identified. At \varOmega = \varOmega_c1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for |loge| << \varOmega < \varOmega_c2 ~ e^-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For \varOmega 3 \varOmega _c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε ⁻²|log ε|⁻¹ vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at \varOmega = \varOmega_c3 ~ e^-2|loge|^-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break rotational symmetry in the whole parameter range, including the giant vortex phase.     

Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons. I.

Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential ${v(x)= \epsilon \chi(x) |x|^{-1}}Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schr?dinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential v(x) = ec(x) |x|^-1{v(x)= \epsilon \chi(x) |x|^{-1}}, where e{\epsilon} is sufficiently small and c ? C₀^￥{\chi \in C_0^{\infty}} even, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and sophisticated estimates for a subsequent part (Part II) of this paper.     

the distribution of exit times for weakly colored noise

We analyze the exit time (first passage time) problem for the Ornstein-Uhlenbeck model of Brownian motion. Specifically, consider the positionX(t) of a particle whose velocity is an Ornstein-Uhlenbeck process with amplitudeσ/ρ and correlation time ε², $$dX/dt = \sigma Z/\varepsilon , dZ/dt = - Z/\varepsilon ^2 + 2^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \xi (t)/\varepsilon $$ whereξ(t) is Gaussian white noise. Let the exit timet _ex be the first time the particle escapes an interval ?A, given that it starts atX(0)=0 withZ(0)=z ₀. Here we determine the exit time probability distributionF(t)≡Prob {t _ex>t} by directly solving the Fokker-Planck equation. In brief, after taking a Laplace transform, we use singular perturbation methods to reduce the Fokker-Planck equation to a boundary layer problem. This boundary layer problem turns out to be a half-range expansion problem, which we solve via complex variable techniques. This yields the Laplace transform ofF(t) to within a transcendentally smallO(e ^?A/εσ +e ^?B/εσ error. We then obtainF(t) by inverting the transform order by order in ε. In particular, by lettingB→∞ we obtain the solution to Wang and Uhlenbeck's unsolved problem b; throughO(ε²σ²/A ¹) this solution is $$F(t) = Erf\left\{ {\frac{{A + \varepsilon \sigma \alpha + \varepsilon \sigma z_0 }}{{2\sigma (t - \varepsilon ^2 \kappa )^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }}} \right\} + ... for \frac{t}{{\varepsilon ^2 }} > > 1$$ andF=1 otherwise. Here, α=∥ξ(1/2)∥=1.4603?, where ξ is the Riemann zeta function, and the constant κ is 0.22749?.     

The Transformations from the New Intermediate Entangled State

The new intermediate entangled state |η;θ〉 is proposed by virtue of IWOP technique, which is the common eigenvector of [([^(x)]₁ - [^(x)]₂)cosq-([^(p)]₁ - [^(p)]₂)sinq][(\hat{x}_{1} - \hat{x}_{2})\cos\theta -(\hat{p}_{1} - \hat{p}_{2})\sin\theta ] and [([^(x)]₁ +[^(x)]₂)sinq+ ([^(p)]₁ + [^(p)]₂)cosq][(\hat{x}_{1} +\hat{x}_{2})\sin\theta + (\hat{p}_{1} + \hat{p}_{2})\cos\theta ]. The squeezing transformation operator, Hadamard transformation operator, Fresnel transformation operator and Radon transform operator are constructed by |η;θ〉.     

Cosmological Post-Newtonian Expansions to Arbitrary Order

We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter e = v_T/c{\epsilon=v_T/c} (0 < e < e₀){(0< \epsilon < \epsilon_0)}, where c is the speed of light, and v _T is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M @ [0,T)×\mathbb T³{M\cong [0,T)\times \mathbb {T}^3}, and converge as e\searrow 0{\epsilon \searrow 0} to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter e{\epsilon} to any specified order with expansion coefficients that satisfy e{\epsilon}-independent (nonlocal) symmetric hyperbolic equations.     

Finite Trotter Approximation to the Averaged Mean Square Distance in the Anderson Model

We prove that a finite Trotter approximation to the averaged mean square distance traveled by a particle in a disordered system on a lattice ℤ ^d exhibits at most a diffusive behavior in dimensions d≥3 as long as the Fourier transform of the single-site probability, [^(m)]\hat{\mu }, is in L ²(ℝ).     

Magnetocaloric properties of as-quenched Ni50.4Mn34.9In14.7 ferromagnetic shape memory alloy ribbons

The temperature dependences of magnetic entropy change and refrigerant capacity have been calculated for a maximum field change of Δ H=30 kOe in as-quenched ribbons of the ferromagnetic shape memory alloy Ni_50.4Mn_34.9In_14.7 around the structural reverse martensitic transformation and magnetic transition of austenite. The ribbons crystallize into a single-phase austenite with the L2₁-type crystal structure and Curie point of 284 K. At 262 K austenite starts its transformation into a 10-layered structurally modulated monoclinic martensite. The first- and second-order character of the structural and magnetic transitions was confirmed by the Arrott plot method. Despite the superior absolute value of the maximum magnetic entropy change obtained in the temperature interval where the reverse martensitic transformation occurs (|\varDelta S_M^max|=7.2 J kg^-1 K^-1)(|\varDelta S_{\mathrm{M}}^{\max}|=7.2\mbox{ J}\,\mbox{kg}^{-1}\,\mbox{K}^{-1}) with respect to that obtained around the ferromagnetic transition of austenite (|\varDelta S_M^max|=2.6 J kg^-1 K^-1)(|\varDelta S_{\mathrm{M}}^{\max}|=2.6\mbox{ J}\,\mbox{kg}^{-1}\,\mbox{K}^{-1}), the large average hysteretic losses due to the effect of the magnetic field on the phase transformation as well as the narrow thermal dependence of the magnetic entropy change make the temperature interval around the ferromagnetic transition of austenite of a higher effective refrigerant capacity (RC^magn_eff=95J kg^-1\mathrm{RC}^{\mathrm{magn}}_{\mathrm{eff}}=95\mbox{J}\,\mbox{kg}^{-1} versus RC^struct_eff=60J kg^-1)\mathrm{RC}^{\mathrm{struct}}_{\mathrm{eff}}=60\mbox{J}\,\mbox{kg}^{-1}).     

On the Mixing Time of the 2D Stochastic Ising Model with “Plus” Boundary Conditions at Low Temperature

We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to +  (equal to ?). For β large enough we show that for any ${\varepsilon >0 }We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to +  (equal to −). For β large enough we show that for any ${\varepsilon >0 }${\varepsilon >0 } there exists c=c(b,e){c=c(\beta,\varepsilon)} such that the corresponding mixing time T _mix satisfies lim_L?￥ P(T_mix 3 exp(cL^e)) = 0{{\rm lim}_{L\to\infty}\,{\bf P}\left(T_{\rm mix}\ge {\rm exp}({cL^\varepsilon})\right) =0}. In the non-random case τ ≡ +  (or τ ≡ −), this implies that T_mix ￡ exp(cL^e){T_{\rm mix}\le {\rm exp}({cL^\varepsilon})}. The same bound holds when the boundary conditions are all +  on three sides and all − on the remaining one. The result, although still very far from the expected Lifshitz behavior T _mix = O(L ²), considerably improves upon the previous known estimates of the form T_mix ￡ exp(c L^{\frac 12 + e}){T_{\rm mix}\le {\rm exp}({c L^{\frac 12 + \varepsilon}})}. The techniques are based on induction over length scales, combined with a judicious use of the so-called “censoring inequality” of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure.     

The mixing of scalar mesons and the baryon-baryon interaction

By introducing the mixing of scalar mesons in the chiral SU(3) quark model, we dynamically investigate the baryon-baryon interaction. The hyperon-nucleon and nucleon-nucleon interactions are studied by solving the resonating group method (RGM) equation in a coupled-channel calculation. In our present work, the experimental lightest pseudoscalar p \pi, K,h \eta,h^￠ \eta^{{\prime}}_{} mesons correspond exactly to the chiral nonet pseudoscalar fields p \pi, K,h \eta,h^￠ \eta^{{\prime}}_{} in the chiral SU(3) quark model. The h \eta,h^￠ \eta^{{\prime}}_{} mesons are considered as the mixing of singlet and octet mesons, and the mixing angle q_ps \theta_{{ps}}^{} is taken to be -23^° . For scalar nonet mesons, we suppose that there exists a correspondence between the experimental lightest scalar f ₀(600) , k \kappa , a ₀(980) , f ₀(980) mesons and the theoretical scalar nonet s \sigma , k \kappa , s^￠ \sigma^{{\prime}}_{} , e \epsilon fields in the chiral SU(3) quark model. For scalar mesons, we consider two different mixing cases: one is the ideal mixing and another is the q_s \theta_{s}^{} = 19^° mixing. The masses of the s^￠ \sigma^{{\prime}}_{} and e \epsilon mesons are taken to be 980MeV, which are just the masses of the experimental a ₀(980) , f ₀(980) mesons. The mass of the s \sigma meson is an adjustable parameter and is decided by fitting the binding energy of the deuteron, the masses of 560MeV and 644MeV are obtained for the ideal mixing and the q_s \theta_{s}^{} = 19^° mixing, respectively. We find that, in order to reasonably describe the YN interactions, the mass of the k \kappa meson is near 780MeV for the ideal mixing. However, we must enhance the mass of the k \kappa meson for the q_s \theta_{s}^{} = 19^° mixing, the 1050MeV is favorably used in the present work. The experimental s \sigma and k \kappa scalar mesons are very strange, both have larger widths. Hence, no matter what kind of mixing is considered, all the masses of scalar mesons we used in the present work seem to be consistent with the present PDG information.     

Macroscopic behavior of systems with an axial dynamic preferred direction

We present the derivation of the macroscopic equations for systems with an axial dynamic preferred direction. In addition to the usual hydrodynamic variables, we introduce the time derivative of the local preferred direction as a new variable and discuss its macroscopic consequences including new cross-coupling terms. Such an approach is expected to be useful for a number of systems for which orientational degrees of freedom are important including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such a Proteus mirabilis. We point out similarities in symmetry between the additional macroscopic variable discussed here, and the magnetization density in magnetic systems as well as the so-called [^(l)]\hat l vector in superfluid ³He-A. Furthermore we investigate the coupling to a gel-like system for which one has the strain tensor and relative rotations between the new variable and the network as additional macroscopic variables.     

A fresh look at hadronic light-by-light scattering in the muon g - 2 with the Dyson-Schwinger approach

Using the Dyson-Schwinger and Bethe-Salpeter equations, we calculate the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon a_m\ensuremath a_\mu , using a phenomenological model for the gluon and quark-gluon interaction. We find a_m=(84 ±13)×10^-11\ensuremath a_\mu=(84 \pm 13)\times 10^{-11} for meson exchange, and a_m = (107 ±2 ±46)×10^-11\ensuremath a_\mu = (107 \pm 2 \pm 46)\times 10^{-11} for the quark loop. The former is commensurate with past calculations; the latter much larger due to dressing effects. This leads to a revised estimate of a_m=116 591 865.0(96.6)×10^-11\ensuremath a_\mu=116 591 865.0(96.6)\times 10^{-11} , reducing the difference between theory and experiment to ≃ 1.9s \sigma .