About a nonadditivity of energy and entropy

The mathematical expression of nonadditivity X(1 ?? 2) = X(1) + X(2) + ??X(1)X(2) has been frequently used for the development of statistical physics for nonadditive system, where X is entropy or energy, and ?? is hoped to be a parameter characterising the nonadditive property of the composite system (1 ?? 2). Here we show that this relationship cannot hold exactly. In general, ?? in this expression inevitably depends on how a given system with constant X(1 ?? 2) is divided into subsystems 1 and 2. Hence mathematical problems may arise when it is used to characterise the nonadditivity of the system. Nevertheless, under some conditions, it is possible to use it as a good approximation.     

Mechanism of pion production in αp scattering at 1 GeV/nucleon

An analysis of the experimental data on one-pion and two-pion production in the p(??, ????)X reaction studied in a semi-exclusive experiment at an energy of E _?? = 4.2 GeV has been performed. The obtained results demonstrate that the inelastic ??-particle scattering on the proton at the energy of the experiment proceeds either through excitation and decay of the ?? resonance in the projectile ?? particle, or through excitation in the target proton of the Roper resonance, which decays into a nucleon and a pion, or a nucleon and a ?? meson??a system of two pions in the isospin I = 0, S-wave state.     

Invariant Measures for Dissipative Dynamical Systems: Abstract Results and Applications

In this work we study certain invariant measures that can be associated to the time averaged observation of a broad class of dissipative semigroups via the notion of a generalized Banach limit. Consider an arbitrary complete separable metric space X which is acted on by any continuous semigroup {S(t)} _{t ?? 0}. Suppose that {S(t)} _{t ?? 0} possesses a global attractor ${\mathcal{A}}$ . We show that, for any generalized Banach limit LIM _{T ?? ??} and any probability distribution of initial conditions ${\mathfrak{m}_0}$ , that there exists an invariant probability measure ${\mathfrak{m}}$ , whose support is contained in ${\mathcal{A}}$ , such that $$\int_{X} \varphi(x) {\rm d}\mathfrak{m}(x) = \underset{t \rightarrow \infty}{\rm LIM}\frac{1}{T} \int_0^T \int_X \varphi(S(t) x) {\rm d}\mathfrak{m}_0(x) {\rm d}t,$$ for all observables ?? living in a suitable function space of continuous mappings on X. This work is based on the framework of Foias et?al. (Encyclopedia of mathematics and its applications, vol 83. Cambridge University Press, Cambridge, 2001); it generalizes and simplifies the proofs of more recent works (Wang in Disc Cont Dyn Syst 23(1?C2):521?C540, 2009; Lukaszewicz et?al. in J Dyn Diff Eq 23(2):225?C250, 2011). In particular our results rely on the novel use of a general but elementary topological observation, valid in any metric space, which concerns the growth of continuous functions in the neighborhood of compact sets. In the case when {S(t)} _{t ?? 0} does not possess a compact absorbing set, this lemma allows us to sidestep the use of weak compactness arguments which require the imposition of cumbersome weak continuity conditions and thus restricts the phase space X to the case of a reflexive Banach space. Two examples of concrete dynamical systems where the semigroup is known to be non-compact are examined in detail. We first consider the Navier-Stokes equations with memory in the diffusion terms. This is the so called Jeffery??s model which describes certain classes of viscoelastic fluids. We then consider a family of neutral delay differential equations, that is equations with delays in the time derivative terms. These systems may arise in the study of wave propagation problems coming from certain first order hyperbolic partial differential equations; for example for the study of line transmission problems. For the second example the phase space is ${X= C([-\tau,0],\mathbb{R}^n)}$ , for some delay ?? > 0, so that X is not reflexive in this case.     

Coupled resonant modes in twisted acoustic metamaterials

Acoustic metamaterials constructed by resonant microelements in subwavelength scale were generally characterized by the effective medium approximation theory, which neglects the interaction between adjacent elements. In this paper, we show that twisting the orientation of resonators in acoustic metamaterials produces secondary coupled resonant modes by introducing internal vibration interaction. Metamaterials composed of a single-slit Helmholtz resonator arranged in two-dimensional square lattice are investigated. We rotate a portion of the resonator so that the adjacent resonators in a ??X direction have a twist angle of ??. For the system with ??=180^°, the coupling interaction produces the symmetric coupled mode in in-phase oscillation and the antisymmetric coupled mode in out-of-phase oscillation. This acoustic analog of ??hybridization effect?? leads to a sharp transparency window in the extended locally-resonant forbidden gap, which is analogous to the phenomenon of electromagnetically induced transparency. Such coupled resonant modes may have potential applications in sound wave manipulations such as acoustic filtering and imaging.     

Investigation of near-threshold eta-meson production in the reaction π ? p→ ηn

Differential and total cross sections for eta-meson production in the reaction ?? ^? p ?? ??n were measured within the experimental program eta-meson physics implemented in the pion channel of the synchrocyclotron of the Petersburg Nuclear Physics Institute (PNPI, Gatchina). These measurements were performed at incident-pion momenta (700, 710, 720, and 730 MeV/c) in the vicinity of the threshold for the process under study by using the neutral-meson spectrometer designed and created at the Meson Physics Laboratory of PNPI. It is shown that, in the immediate vicinity of the threshold (685 MeV/c), the process of eta-meson production proceeds predominantly via S ₁₁(1535)-resonance formation followed by the decay S ₁₁(1535) ?? ??n (the respective branching fraction is Br ?? 60%), but that, as the momentum of incident pions increases, the role of the D wave becomes ever more important. A detailed analysis of this effect indicates that it is due to the increasing contribution of the D ₁₃(1520) resonance. Although the branching fraction of the decay of this resonance through the ??n channel is assumed to be very small (BR ?? 0.24%), the effect is enhanced owing to the interference between the D wave and the dominant resonance S ₁₁(1535).     

Star Products with Separation of Variables Admitting a Smooth Extension

Given a complex manifold M with an open dense subset ?? endowed with a pseudo-K?hler form ?? which cannot be smoothly extended to a larger open subset, we consider various examples where the corresponding K?hler?CPoisson structure and a star product with separation of variables on (??, ??) admit smooth extensions to M. We give a simple criterion of the existence of a smooth extension of a star product and apply it to these examples.     

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.      

Third-harmonic generation in relative-phase-controlled two-color laser field

We experimentally demonstrate third-harmonic generation (THG) by intense femtosecond laser pulse at a central wavelength of ??800?nm superposed by its second harmonic in air. The third-harmonic signal shows a periodic modulation with a period of ??0.67?fs when the delay between fundamental and second-harmonic wave is continuously changed. The periodic modulation of THG can be attributed to the interference of third-harmonic signals generated from a direct THG channel (3??=??+??+??) and a four-wave mixing (FWM) channel (3??=2??+2?????). With high pump intensity, the fitting of the measured TH spectrum as a function of delay implies that the pump pulse undergoes a strong pulse splitting and self-phase modulation at the focus.     

���Ѧ� Interaction Leading to N* and ��* Resonances

We have performed a calculation for the three-body ????? system by using the fixed center approximation to Faddeev equations, taking the interaction between ?? and ??, ?? and ??, and ?? and ?? from the chiral unitary approach. We find several peaks in the modulus squared of the three-body scattering amplitude, indicating the existence of resonances, which can be associated to known I?=?1/2, 3/2 and J ^P ?=?1/2⁺, 3/2⁺ and 5/2⁺ baryon states.     

A Markovian Growth Dynamics on Rooted Binary Trees Evolving According to the Gompertz Curve

Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields (Probab. Theory Relat. Fields 79(4):509?C542, 1988) model. Fix n??1 and ??>0. We start at time 0 with the tree composed of a root only. At any time, each node with no descendants, independently from the other nodes, produces two successors at rate ??(n?k)/n, where k is the distance from the node to the root. Denote by Z _n (t) the number of nodes with no descendants at time t and let T _n =?? ^?1 nln(n/ln4)+(ln2)/(2??). We prove that 2^?n Z _n (T _n +n??), ?????, converges to the Gompertz curve exp(?(ln2)?e ^??|? ). We also prove a central limit theorem for the martingale associated to Z _n (t).     

The equivalent photon approximation for coherent processes at colliders

We consider coherent electromagnetic processes for colliders with short bunches, in particular the coherent bremsstrahlung (CBS). CBS is the radiation of one bunch particles in the collective field of the oncoming bunch. It can be a potential tool for optimizing collisions and for measuring beam parameters. A new simple and transparent method to calculate CBS is presented based on the equivalent photon approximation for this collective field. The results are applied to the??-factoryDA??NE. For this collider about 5·10¹⁴ d E _??/E _?? photons per second are expected in the photon energyE _?? range from the visible light up to 25 eV.     

Exponential smoothing weighted correlations

In many practical applications, correlation matrices might be affected by the ??curse of dimensionality?? and by an excessive sensitiveness to outliers and remote observations. These shortcomings can cause problems of statistical robustness especially accentuated when a system of dynamic correlations over a running window is concerned. These drawbacks can be partially mitigated by assigning a structure of weights to observational events. In this paper, we discuss Pearson??s ?? and Kendall??s ?? correlation matrices, weighted with an exponential smoothing, computed on moving windows using a data-set of daily returns for 300 NYSE highly capitalized companies in the period between 2001 and 2003. Criteria for jointly determining optimal weights together with the optimal length of the running window are proposed. We find that the exponential smoothing can provide more robust and reliable dynamic measures and we discuss that a careful choice of the parameters can reduce the autocorrelation of dynamic correlations whilst keeping significance and robustness of the measure. Weighted correlations are found to be smoother and recovering faster from market turbulence than their unweighted counterparts, helping also to discriminate more effectively genuine from spurious correlations.     

Disordering effects in the atomic structure of fine-crystalline HTSC YBa2Cu3O y

The atomic structure of YBa₂Cu₃O _y fine-crystalline HTSC samples with various average crystallite sizes ??D?? ranging from 0.4 to 2 ??m and an oxygen concentration y close to the optimal value for superconductivity (y ?? 6.93) is investigated by the neutron diffraction technique. We have found some effects associated with the redistribution of cations and oxygen atoms and with variations in the positions of atomic layers in the unit cell, which are not observed in macrocrystalline samples. In all probability, these effects appear due to nonequilibrium conditions of synthesis required for obtaining this compound in the fine-crystalline state. The results have made it possible to explain the peculiar physical properties of fine-crystalline YBa₂Cu₃O _y samples (in particular, the coexistence of high superconducting transition temperatures T _c and noticeably lower values of magnetization in strong magnetic fields for T < T _c ). It is shown that a nanoscale structural inhomogeneity exists in fine-crystalline YBa₂Cu₃O _y samples with the optimal oxygen content and changes the fundamental superconducting parameters, viz., the magnetic field penetration depth and the coherence length.     

AnomalousZ�� effects in the WW channel at NLC

We consider the virtual signals of aZ?? of very general type in the processe ⁺ e ^???W ⁺ W ^? at a future linear collider (NLC). We show that possible deviations from the SM predictions in this channel are related to similar deviations in the purely leptonic one in a way that is only characteristic of thisZ?? model, and not in general of possible competitor models with anomalous gauge couplings.     

Linear and nonlinear liftings of states of quantum systems

In this paper, we study the representability of an arbitrary quantum state ?? ?? ??(H) as the reduction of a vector state r ?? ??(H) of the extended system. We extend the operation of lifting from the set of states ?? _n (H) to the set of generalized states ??(H). A method of constructing the Hilbert space H and the affine linear lifting ??(H) ?? ??(H) is studied. The construction of individual expansion H _?? of the space H for which the state ?? is a reduction of a vector state H _?? is of special interest.     

Search for exotic meson and hyperon final states in K-d interactions at 5.5 Gev/c

A search has been made for exotic states produced in K^?d interactions at 5.5 GeV/c. The reactions investigated were: K^?d→X^??pp, $\text{K}{}^{\mathrm{?}}\text{d}\text{→}\text{Y}{}^{\mathrm{1??}}\text{π}{}^{\mathrm{+}}\text{p}$ and K^?d→ M^??Σ⁺p. Upper limits are set for the production cross sections.     

Viscosity of the QGP from a virial expansion

In this work we calculate the shear viscosity ?? in the quark-gluon plasma within a virial expansion approach with particular interest in the ratio of ?? to the entropy density s, i.e. ??/s. We derive a realistic equation of state using a virial expansion approach which allows us to include the interactions between the partons in the deconfined phase. From the interaction we directly extract the effective coupling ?? _V for the determination of ??. Our results for ??/s show a minimum near to T _c very close with the lowest bound and, furthermore, in line with the experimental point from RHIC as well as with the lattice calculations.     

Glauber Dynamics for the Mean-Field Potts Model

We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with q??3 states and show that it undergoes a critical slowdown at an inverse-temperature ?? _s (q) strictly lower than the critical ?? _c (q) for uniqueness of the thermodynamic limit. The dynamical critical ?? _s (q) is the spinodal point marking the onset of metastability. We prove that when ??<?? _s (q) the mixing time is asymptotically C(??,q)nlogn and the dynamics exhibits the cutoff phenomena, a sharp transition in mixing, with a window of order n. At ??=?? _s (q) the dynamics no longer exhibits cutoff and its mixing obeys a power-law of order n ^4/3. For ??>?? _s (q) the mixing time is exponentially large in n. Furthermore, as ?????? _s with n, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of O(n ^?2/3) around ?? _s . These results form the first complete analysis of mixing around the critical dynamical temperature??including the critical power law??for a model with a first order phase transition.     

Phase space analysis of interacting dark energy in f(T) cosmology

In this paper, we examine the interacting dark energy model in f(T) cosmology. We assume dark energy as a perfect fluid and choose a specific cosmologically viable form f(T) = ????T. We show that there is one attractor solution to the dynamical equation of f(T) Friedmann equations. Further we investigate the stability in phase space for a general f(T) model with two interacting fluids. By studying the local stability near the critical points, we show that the critical points lie on the sheet u* = (c ? 1)v* in the phase space, spanned by coordinates (u, v, ??, T). From this critical sheet, we conclude that the coupling between the dark energy and matter c ?? (?2, 0).