Non-normal tracer diffusion from stirring by swimming microorganisms

The experimentally observed non-Gaussian form of passive tracer distributions in media stirred by active swimmers (Leptos et al., Phys. Rev. Lett. 103, 198103 (2009)) are analyzed in terms of continuous time random walks. The walks are characterized by a trapping time distribution ??(??) with long time behaviour ??(??) ?? ?? ^?1??? and a step size distribution p(??x) ?? (??x)^?2??? . The experimentally observed behaviour that ??x ²?? ?? t is obtained for a one-parameter family of exponents with ?? = 2??. However, the distribution function for this case is non-Gaussian and shows exponential tails. The shape of the distributions agrees rather well with the experimental observations from Leptos et al. and allows for the determination of the exponents.      

Strictly two-dimensional self-avoiding walks: Thermodynamic properties revisited

The density crossover scaling of various thermodynamic properties of solutions and melts of self-avoiding and highly flexible polymer chains without chain intersections confined to strictly two dimensions is investigated by means of molecular dynamics and Monte Carlo simulations of a standard coarse-grained bead-spring model. In the semidilute regime we confirm over an order of magnitude of the monomer density ?? the expected power law scaling for the interaction energy between different chains e _int ?? ?? ^21/8, the total pressure P ?? ?? ³ and the dimensionless compressibility gT = lim _q??0 S(q) ?? 1/?? ². Various elastic contributions associated to the affine and non-affine response to an infinitesimal strain are analyzed as functions of density and sampling time. We show how the size ??(??) of the semidilute blob may be determined experimentally from the total monomer structure factor S(q) characterizing the compressibility of the solution at a given wave vector q . We comment briefly on finite persistence length effects.      

Stuck in traffic: Patterns of powder adhesion

The adhesion of fine particles to surfaces is important for applications ranging from drug delivery to fouling of solar cells. In this letter, we show that powder adhesion can occur in unexpected patterns, concentrating particular grain types in some locations and clearing them from others, and we propose a straightforward traffic model that appears to reproduce many of the behaviors seen. The model predicts different patterns depending on inter-particle cohesion, and we find in both experiment and model that adhesion occurs in three distinct stages.      

Motions of vortex patches

An evolution equation describing the motion of vortrex patches is established. The existence of steady solutions of this equation is proved. These solutions arem-fold symmetric regions of constant vorticity ω₀ and are uniformly rotating with angular velocity Ω in the range $$\tilde \Omega _{m - 1}< \tilde \Omega \leqslant \tilde \Omega _m (\tilde \Omega = \Omega /\omega _0 ,m \geqslant 2)$$ where \(\tilde \Omega _m = (m - 1)/2m\) . We call this class, ofm-fold symmetric rotating regionsD, the class of them-waves of Kelvin. Any may be regarded as a simply connected region which is a stationary configuration of the Euler equations in two dimensions. If then any magnification, rotation or reflection is also in with the same angular velocity Ω ofD. The angular velocity \(\Omega _m = \tilde \Omega _m \omega _0 \) corresponds only to the circle solution, which is a trivial member of every class ,m?2. The class corresponds to the rotating ellipses of Kirchoff. Other properties of the class are established.     

Reverse buoyancy in a vibrated granular bed: Computer simulations

We have performed molecular dynamics simulations of an intruder in a vibrated granular bed including interstitial fluid effects to account for the phenomenon of reverse buoyancy. We show that our model is able to reproduce the overall behaviour observed by previous experimental works and is the first finite-elements simulation to show the sinking of intruders lighter than the granular bed. To further advance our comprehension of this phenomenon, we studied the motion of the intruders in a single vibration cycle with respect to the bottom of the granular column, finding a substantial qualitative difference for heavy and light intruders and we compare these results with experiments using fine-sized glass beads. We show that, though heavy intruders seem unaffected by the force due to the fluid, the effect on light intruders is remarkable.      

Counting Function Fluctuations and Extreme Value Threshold in Multifractal Patterns: The Case Study of an Ideal 1/f Noise

Motivated by the general problem of studying sample-to-sample fluctuations in disorder-generated multifractal patterns we attempt to investigate analytically as well as numerically the statistics of high values of the simplest model??the ideal periodic 1/f Gaussian noise. Our main object of interest is the number of points $\mathcal{N}_{M}(x)$ above a level $\frac{x}{2}V_{m}$ , with V _m =2lnM standing for the leading-order typical value of the absolute maximum for the sample of M points. By employing the thermodynamic formalism we predict the characteristic scale and the precise scaling form of the distribution of $\mathcal{N}_{M}(x)$ for 0<x<2. We demonstrate that the powerlaw forward tail of the probability density, with exponent controlled by the level x, results in an important difference between the mean and the typical values of $\mathcal{N}_{M}(x)$ . This can be further used to determine the typical threshold x _m of extreme values in the pattern which turns out to be given by $x_{m}^{(\mathit{typ})}=2-c\ln\ln M /\ln M $ with $c=\frac{3}{2}$ . Such observation provides a rather compelling explanation of the mechanism behind universality of c. Revealed mechanisms are conjectured to retain their qualitative validity for a broad class of disorder-generated multifractal fields. In particular, we predict that the typical value of the maximum p _max of intensity is to be given by $-\ln p_{\mathit{max}}=\alpha_{-}\ln M +\frac{3}{2f'(\alpha_{-})}\ln\ln M+O(1)$ , where f(??) is the corresponding singularity spectrum positive in the interval ????(?? _?,?? ₊) and vanishing at ??=?? _?>0. For the 1/f noise case we further study asymptotic values of the prefactors in scaling laws for the moments of the counting function. Our numerics shows however that one needs prohibitively large sample sizes to reach such asymptotics even with a moderate precision. This motivates us to derive exact as well as well-controlled approximate formulas for the mean and the variance of the counting function without recourse to the thermodynamic formalism.     

Physics beyond the Standard Model through b → s μ ?+? μ ? transition

A comprehensive study of the impact of new-physics operators with different Lorentz structures on decays involving the b ?? s ?? ^?+? ?? ^? transition is performed. The effects of new vector?Caxial vector (VA), scalar?Cpseudoscalar (SP) and tensor (T) interactions on the differential branching ratios, forward?Cbackward asymmetries (A _FB??s), and direct CP asymmetries of ${\bar B}_{\rm s}^0 \to \mu^+ \mu^-$ , ${\bar B}_{\rm d}^0 \to$ $ X_{\rm s} \mu^+ \mu^-$ , ${\bar B}_{\rm s}^0 \to \mu^+ \mu^- \gamma$ , ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ , and ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ are examined. In ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ , we also explore the longitudinal polarization fraction f _L and the angular asymmetries $A_{\rm T}^{(2)}$ and A _LT, the direct CP asymmetries in them, as well as the triple-product CP asymmetries $A_{\rm T}^{\rm (im)}$ and $A^{\rm (im)}_{\rm LT}$ . While the new VA operators can significantly enhance most of the observables beyond the Standard Model predictions, the SP and T operators can do this only for A _FB in ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ .     

How flow changes polymer depletion in a slit

A theoretical model is developed for predicting dynamic polymer depletion under the influence of fluid flow. The results are established by combining the two-fluid model and the self-consistent field theory. We consider a uniform fluid flow across a slit containing a solution with polymer chains. The two parallel and infinitely long walls are permeable to solvent only and the polymers do not adsorb to these walls. For a weak flow and a narrow slit, an analytic expression is derived to describe the steady-state polymer concentration profiles in a $ \Theta$ -solvent. In both $ \Theta$ - and good-solvents, we compute the time evolution of the concentration profiles for various flow rates characterized by the Peclet number. The model reveals the interplay of depletion, solvent condition, slit width, and the relative strength of the fluid flow.      

Inelastic Character of Solitons of Slowly Varying gKdV Equations

In this paper we study soliton-like solutions of the variable coefficients, the subcritical gKdV equation $$u_t + (u_{xx} -\lambda u + a(\varepsilon x) u^m )_x =0,\quad {\rm in} \quad \mathbb{R}_t\times\mathbb{R}_x, \quad m=2,3\,\, { \rm and }\,\, 4,$$ with ${\lambda\geq 0, a(\cdot ) \in (1,2)}$ a strictly increasing, positive and asymptotically flat potential, and ${\varepsilon}$ small enough. In previous works (Mu?oz in Anal PDE 4:573?C638, 2011; On the soliton dynamics under slowly varying medium for generalized KdV equations: refraction vs. reflection, SIAM J. Math. Anal. 44(1):1?C60, 2012) the existence of a pure, global in time, soliton u(t) of the above equation was proved, satisfying $$\lim_{t\to -\infty}\|u(t) - Q_1(\cdot -(1-\lambda)t) \|_{H^1(\mathbb{R})} =0,\quad 0\leq \lambda<1,$$ provided ${\varepsilon}$ is small enough. Here R(t, x) := Q _c (x ? (c ? ??)t) is the soliton of R _t +? (R _xx ??? R + R ^m ) _x =?0. In addition, there exists ${\tilde \lambda \in (0,1)}$ such that, for all 0?<??? <?1 with ${\lambda\neq \tilde \lambda}$ , the solution u(t) satisfies $$\sup_{t\gg \frac{1}{\varepsilon}}\|u(t) - \kappa(\lambda)Q_{c_\infty}(\cdot-\rho(t)) \|_{H^1(\mathbb{R})}\lesssim \varepsilon^{1/2}.$$ Here ${{\rho'(t) \sim (c_\infty(\lambda) -\lambda)}}$ , with ${{\kappa(\lambda)=2^{-1/(m-1)}}}$ and ${{c_\infty(\lambda)>\lambda}}$ in the case ${0<\lambda<\tilde\lambda}$ (refraction), and ${\kappa(\lambda) =1}$ and c _??(??)?<??? in the case ${\tilde \lambda<\lambda<1}$ (reflection). In this paper we improve our preceding results by proving that the soliton is far from being pure as t ?? +???. Indeed, we give a lower bound on the defect induced by the potential a(·), for all ${{0<\lambda<1, \lambda\neq \tilde \lambda}}$ . More precisely, one has $$\liminf_{t\to +\infty}\| u(t) - \kappa_m(\lambda)Q_{c_\infty}(\cdot-\rho(t)) \|_{H^1(\mathbb{R})}>rsim \varepsilon^{1 +\delta},$$ for any ${{\delta>0}}$ fixed. This bound clarifies the existence of a dispersive tail and the difference with the standard solitons of the constant coefficients, gKdV equation.     

An efficient and facile synthesis of 3-amino-5-chromenyl-butenolides from 3-formyl chromone, dialkyl acetylenedicarboxylate, and primary amines

A three-component reaction of 3-formyl chromones, dialkyl acetylenedicarboxylate, and isocyanides in the presence of $\text{ POCl}_{3}$ was used as a highly efficient and practical approach for the synthesis of 3-amino-5-chromenyl-butenolides. High yields and high bond forming efficiency, and simple operations are the advantages of this method. Graphical abstract      

Feynman's path integral

Feynman's integral is defined with respect to a pseudomeasure on the space of paths: for instance, letC be the space of pathsq:T?? → configuration space of the system, letC be the topological dual ofC; then Feynman's integral for a particle of massm in a potentialV can be written where $$S_{\operatorname{int} } (q) = \mathop \smallint \limits_T V(q(t)) dt$$ and wheredw is a pseudomeasure whose Fourier transform is defined by for μ∈C′. Pseudomeasures are discussed; several integrals with respect to pseudomeasures are computed.     

Flavoured co-annihilation

In minimal supergravity (mSUGRA) or CMSSM, one of the main co-annihilating partners of the neutralino is the lightest stau, $\tilde{\tau}_1$ . In the presence of flavour violation in the right-handed sector, the co-annihilating partner would be a flavour mixed state. The flavour effect is two-fold: (a) It changes the mass of $\tilde{\tau}_{1}$ , thus modifying the parameter space of the co-annihilation and (b) flavour violating scatterings could now contribute to the cross-sections in the early Universe. In fact, it is shown that for large enough ??~0.2, these processes would constitute the dominant channels in co-annihilation regions. The amount of flavour mixing permissible is constrained by flavour violating ?????? or ????e processes. For ??_RR mass insertions, the constraints from flavour violation are not strong enough in some regions of the parameter space due to partial cancellations in the amplitudes. In mSUGRA, the regions with cancelations within LFV amplitudes do not overlap with the regions of co-annihilations. In non-universal Higgs model (NUHM), however, these regions do overlap leading to significant flavoured co-annihilations. At the LHC and other colliders, these regions can constitute for interesting signals.     

Galaxy cluster number count data constraints on cosmological parameters

We use data on massive galaxy clusters (M _cluster>8×10¹⁴ h ^?1 M _?? within a comoving radius of R _cluster=1.5h ^?1?Mpc) in the redshift range 0.05?z?0.83 to place constraints, simultaneously, on the nonrelativistic matter density parameter ?? _m , on the amplitude of mass fluctuations ?? ₈, on the index n of the power-law spectrum of the density perturbations, and on the Hubble constant H ₀, as well as on the equation-of-state parameters (w ₀,w _a ) of a smooth dark energy component. For the first time, we properly take into account the dependence on redshift and cosmology of the quantities related to cluster physics: the critical density contrast, the growth factor, the mass conversion factor, the virial overdensity, the virial radius and, most importantly, the cluster number count derived from the observational temperature data. We show that, contrary to previous analyses, cluster data alone prefer low values of the amplitude of mass fluctuations, ?? ₈??0.69 (1?? C.L.), and large amounts of nonrelativistic matter, ?? _m ??0.38 (1?? C.L.), in slight tension with the ??CDM concordance cosmological model, though the results are compatible with ??CDM at 2??. In addition, we derive a ?? ₈ normalization relation, $\sigma_{8} \varOmega_{m}^{1/3} = 0.49 \pm 0.06$ (2?? C.L.). Combining cluster data with ?? ₈-independent baryon acoustic oscillation observations, cosmic microwave background data, Hubble constant measurements, Hubble parameter determination from passively evolving red galaxies, and magnitude?Credshift data of type Ia supernovae, we find $\varOmega_{m} = 0.28^{+0.03}_{-0.02}$ and $\sigma_{8} = 0.73^{+0.03}_{-0.03}$ , the former in agreement and the latter being slightly lower than the corresponding values in the concordance cosmological model. We also find $H_{0} = 69.1^{+1.3}_{-1.5}~\mbox {km}/\mbox {s}/\mbox {Mpc}$ , the fit to the data being almost independent on n in the adopted range [0.90,1.05]. Concerning the dark energy equation-of-state parameters, we show that the present data on massive clusters weakly constrain (w ₀,w _a ) around the values corresponding to a cosmological constant, i.e. (w ₀,w _a )=(?1,0). The global analysis gives $w_{0} = -1.14^{+0.14}_{-0.16}$ and $w_{a} = 0.85^{+0.42}_{-0.60}$ (1?? C.L. errors). Very similar results are found in the case of time-evolving dark energy with a constant equation-of-state parameter w=const (the XCDM parametrization). Finally, we show that the impact of bounds on (w ₀,w _a ) is to favor top-down phantom models of evolving dark energy.     

On a symmetry topological classification of edge states in crystalline spin-Hall insulators with the time reversal invariance

Symmetry analysis reveals all types of singularities of the edge states in two-dimensional systems with a boundary (2D → 1D systems), which are invariant under time reversal. Symmetry reasons also provide the matching condition for material functions parameterizing the Hamiltonian at various points of the Brillouin zone. The unified parameterization of the Hamiltonian makes it possible to construct the mapping of trajectories closed in the quasimomentum k in the Brillouin zone into the SU(2) topological group. There are only two equivalence classes of Hamiltonians, which are given by the elements of the first fundamental group . The first type of surface states corresponds to a normal insulator and the second type corresponds to a topological spin-Hall insulator. Comparison with the classification based on the Pfaffian method is performed.     

Smectic order parameters via liquid crystal NMR spectroscopy: Application to a partial bilayer smectic A phase

Solute molecules were dissolved in the liquid crystal 4-cyano-4??-n-octyloxybiphenyl (8OCB), known to form a partial bilayer smectic-A phase. Through measurement of solutes?? and solvent??s orientational order parameters via nuclear magnetic resonance spectroscopy, and their analysis via a statistical thermodynamic density functional theory, values of the solvent??s positional order parameters and solutes?? positional-orientational distribution functions were obtained. Near to the transition to the nematic phase, the main positional order parameter of the smectic liquid crystal turned out to be comprised in the interval 0.4?C0.6, though the quality of the fittings assuming the phase as nematic all across the temperature range investigated was only slightly worse. This may be ascribed to the looseness of the partial bilayer smectic structure. Solutes were found to preferentially lie in those regions where liquid crystal molecule terminal chains are located.      

Structure and dynamics of a polymer melt at an attractive surface

We study the structural and dynamic properties of a polymer melt in the vicinity of an adhesive solid substrate by means of Molecular Dynamics simulation at various degrees of surface adhesion. The properties of the individual polymer chains are examined as a function of the distance to the interface and found to agree favorably with theoretical predictions. Thus, the adsorbed amount at the adhesive surface is found to scale with the macromolecule length as $\Gamma \propto \sqrt N$ , regardless of the adsorption strength. For chains within the range of adsorption we analyze in detail the probability size distributions of the various building blocks: loops, tails and trains, and find that loops and tails sizes follow power laws while train lengths decay exponentially thus confirming some recent theoretical results. The chain dynamics as well as the monomer mobility are also investigated and found to depend significantly on the proximity of a given layer to the solid adhesive surface with onset of vitrification for sufficiently strong adsorption.      

N,N,N^{\prime },N^{\prime }-Tetrabromobenzene-1,3-disulfonamide and poly(N-bromo-N-ethylbenzene-1,3-disulfonamide) as new and efficient catalysts for the synthesis of highly substituted 1,6-dihydropyrazine-2,3-dicarbonitrile derivatives

Various mono and bis-1,6-dihydropyrazine-2,3-dicarbonitrile derivatives were efficiently synthesized by reacting 2,3-diaminomaleonitrile (DAMN), isocyanides and ketones in the presence of a catalytic amount of $N,N{,}N^{\prime }{,}N^{\prime }$ -tetrabromobenzene-1,3-disulfonamide [TBBDA] and poly( $N$ -bromo- $N$ -ethylbenzene-1,3-disulfonamide) [PBBS] in EtOH/H $_{2}$ O at ambient temperature. Graphic abstract $N,N,N^{\prime },N^{\prime }$ -Tetrabromobenzene-1,3-disulfonamide and poly( $N$ -bromo- $N$ -ethylbenzene-1,3-disulfonamide) as new and efficient catalysts for the synthesis of highly substituted 1,6-dihydropyrazine-2,3-dicarbonitrile derivatives.      

Mesoscopic models for DNA stretching under force: New results and comparison with experiments

We investigate the dynamical behavior of simple networks, namely loops with an additional internal regulating connection. Continuous dynamics for mRNA and protein concentrations is compared to a Boolean model for gene activity. Using a generalized method and within a single framework, we study different continuous models and different types of regulatory functions, and establish conditions under which the system can display stable oscillations or stable fixed points. These conditions depend only on general features such as the degree of cooperativity of the regulating interactions and the logical structure of the interactions. There are no simple rules for deciding when Boolean and continuous dynamics agree with each other, but we identify several relevant criteria.      

Jack Superpolynomials with Negative Fractional Parameter: Clustering Properties and Super-Virasoro Ideals

The Jack polynomials ${P_\lambda^{(\alpha)}}$ at ???= ?(k?+?1)/(r ? 1) indexed by certain (k, r, N)-admissible partitions are known to span an ideal ${I_{N}^{(k,r)}}$ of the space of symmetric functions in N variables. The ideal ${I_{N}^{(k,r)}}$ is invariant under the action of certain differential operators which include half the Virasoro algebra. Moreover, the Jack polynomials in ${I_{N}^{(k,r)}}$ admit clusters of size at most k: they vanish when k?+?1 of their variables are identified, and they do not vanish when only k of them are identified. We generalize most of these properties to superspace using orthogonal eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular, we show that the Jack superpolynomials ${P_\lambda^{(\alpha)}}$ at ???= ?(k?+?1)/(r ? 1) indexed by certain (k, r, N)-admissible superpartitions span an ideal ${\mathcal{I}_{N}^{(k,r)}}$ of the space of symmetric polynomials in N commuting variables and N anticommuting variables. We prove that the ideal ${\mathcal{I}_{N}^{(k,r)}}$ is stable with respect to the action of the negative-half of the super-Virasoro algebra. In addition, we show that the Jack superpolynomials in ${\mathcal {I}_{N}^{(k,r)}}$ vanish when k?+?1 of their commuting variables are equal, and conjecture that they do not vanish when only k of them are identified. This allows us to conclude that the standard Jack polynomials with prescribed symmetry should satisfy similar clustering properties. Finally, we conjecture that the elements of ${\mathcal{I}_{N}^{(k,2)}}$ provide a basis for the subspace of symmetric superpolynomials in N variables that vanish when k?+?1 commuting variables are set equal to each other.     

Parity-violating asymmetry in the reactions 6Li(n,\alpha) 3H and 10B(n,\alpha)^{7}Li* \rightarrow 7Li + \gamma

We present two experiments measuring the parity-violating asymmetry (P-odd) of tritons emission in the reaction ⁶Li(n,??)³H and ??-quanta emission in the reaction ¹⁰B(n,??)⁷Li* ?? ⁷Li + ?? with polarized cold neutrons, aiming at estimation of the weak meson-nucleon coupling constants. These experiments started in the PNPI, Gatchina and continued in the ILL, Grenoble. We describe an integral method to measure P-odd asymmetry and the two experiments. The results of our measurements are: $\alpha{}_{P-odd}^{6Li}=(-8.8\pm2.1)\cdot10^{-8}$ and $\alpha{}_{P-odd}^{10B}=(0.8\pm3.9)\cdot10^{-8}$ .