Determination of the physical network of entanglements and the molecular mobility in linear flexible polymers by the NMR method

In the present paper, a theory of free induction decay in linear flexible chain polymers is developed. Theoretical and experimental dependences of the spin-spin relaxation time T ₂ on the average molecular weight M _w and temperature are compared. It is shown that, with increasing M _w , the topological structure of linear polymers changes, and at M _w > 10⁵, a physical network entanglements (quasi-network) is formed. A correlation function of molecular motions is obtained, which indicates whether the quasi-network is formed in polymer melts.     

The effect of Higgses and “technions” on the calculation of sin2θw and Mx

The effect of the scalar sector on the calculation of sin²θ_w and M_x in grand unified theories is studied. We consider first elementary Higgs scalars and assume the “big desert” hypothesis. It is argued that Higgses other than the usual doublet can also be light (～ M_w). One can obtain bigger values for sin²θ_w by having light (～ M_w) scalar colour sextets which can give rise to interesting phenomenology. As an example, one can build an SU(5) model giving sin²θ_w ? 0.23 at the one-loop level. We also calculate the uncertainty in sin²θ_w and M_x due to the lack of knowledge of the specific masses of superheavy Higgses. We find that this uncertainty is small for reasonable SU(5) models but large in all the SO(10) versions except the minimal. Finally (and alternatively) we consider the effect of a technicolour interaction. The pseudo-Goldstone bosons (technions) increase the calculated sin²θ_w by as much as ～0.01 but M_x remains nearly unchanged. Second-order contributions due to the technifermions tend to cancel the increase on sin²θ_w and in turn increase M_x.     

Paramagnetic–ferrimagnetic transition in strong coupling paramagnetic systems: effect of cubic anisotropy interaction

The purpose of the present work is a quantitative investigation of the biquadratic exchange interaction effects on the paramagnetic–ferrimagnetic transition arising from two strongly coupled paramagnetic (1-spin) sublattices, of respective moments m and M. The free energy describing the physics of the system is of Landau type. In addition to the quadratic and quartic terms, in both m and M, this free energy involves two mixing interaction terms. The first is a lowest order coupling −CmM, where C<0 stands for the coupling constant measuring the interaction between the two sublattices. While the second, which is relevant for 1-spin systems and which traduces the dipole–dipole (or biquadratic) interaction, is of type wm²M², where w>0 is the new coupling constant. These two interactions enter in competition, and then, they induce drastic changes of the magnetic behavior of the material. The main change is that, the presence of this high order coupling tends to destroy the ferrimagnetic order of the system. We first show that the introduction of this biquadratic interaction does not affect the values of critical exponents. Also, we find that the compensation temperature (when it exists) and the compensation magnetic field are shifted to their lowest values, in comparison with the w=0 case. The Arrott-phase-diagram shape is also investigated quantitatively. We show the existence of three regimes depending on the values of w. When the latter is small, we find that the region of competition between the coupling C and the applied magnetic field H becomes more narrow under the effect of w (by competition, we mean the passage from the antiparallel state to the parallel one). While for higher values of w, this competition disappears completely, and then, the system loses its ferrimagnetic character. Kinetics of the phase transition is also examined, when the temperature is lowered from an initial value T_i to a final one T_f very close to the critical temperature T_c. As in the w=0 case, we find that kinetics is controlled by two kinds of relaxation times τ₁ and τ₂. The former is the relevant time, and is associated to long-wavelength fluctuations driving the system to undergo a phase transition. The second is a short time, which controls local dynamics. Near T_c, we show that, in particular, the longest relaxation time τ₁ becomes less important in comparison with that relative to the w=0 case. Finally, we note that the existence of two relaxation times is consistent with the predictions of a recent experiment, which was concerned with the 1/2-spin compounds Li_xNi_2−xO₂, where the composition x is close to 1.     

NMR determination of topological structure and self-diffusion of linear polymers

A general approach is proposed to calculate the attenuation of spin echo diffusion and the self-diffusion coefficients D of linear polymers with different average molecular weights M _w . It was shown that the changes in the topological structure of linear polymers resulted from the formation of a physical entanglement network at M _w > 10⁵ are responsible for the experimentally observed anomalous diffusion D(M _w ).     

Ultrasonic assisted water-in-oil emulsions encapsulating macro-molecular polysaccharide chitosan: Influence of molecular properties,emulsion viscosity and their stability

An ultrasonic technique was applied to formulation of two-phase water-in-paraffin oil emulsions loading a high-molecular polysaccharide chitosan (CS) and stabilized by an oil-soluble surfactant (Span80) at different operational conditions. The influence of chitosan molecular properties, phase volume ratio (φ_w), Span80 volume fraction (φ_s) and ultrasonic processing parameters were systemically investigated on the basis of mean droplet diameter (MDD) and polydispersity index (PDI) of emulsions. It was observed that the molecular weight (M_w) of CS was an important influential factor to MDD due to the non-Newtonian properties of CS solution varying with M_w. The minimum MDD of 198.5 nm with PDI of 0.326 was obtained with ultrasonic amplitude of 32% for 15 min at an optimum φ_w of 35%, φ_s of 8%, probe position of 2.2 cm to the top of emulsion, while CS with M_w of 400 kDa and deacetylation degree of 84.6% was used. The rise of emulsion viscosity and the reduction of negative zeta potential at φ_w increasing from 5% to 35% were beneficial to obtain finer droplets and more uniform distribution of emulsions, and emulsion viscosity could be represented as a monotonically-decreasing power function of MDD at the same φ_w. FTIR analysis indicated that the molecular structure of paraffin oil was unaffected during ultrasonication. Moreover, the emulsions exhibited a good stability at 4 °C with a slight phase separation at 25 °C after 24 h of storage. By analyzing the evolution of MDD, PDI and sedimentation index (SI) with time, coalescence model showed better fitting results as comparison to Ostwald ripening model, which demonstrated that the coalescence or flocculation was the dominant destabilizing mechanism for such W/O emulsions encapsulating CS. This study may provide a valuable contribution for the application of a non-Newtonian macromolecule solution as dispersed phase to generate nano-size W/O emulsions via ultrasound, and widen knowledge and interest of such emulsions in the functional biomaterial field.     

Extremes of N Vicious Walkers for Large N: Application to the Directed Polymer and KPZ Interfaces

We compute the joint probability density function (jpdf) P _N (M,?? _M ) of the maximum M and its position ?? _M for N non-intersecting Brownian excursions, on the unit time interval, in the large N limit. For N????, this jpdf is peaked around $M = \sqrt{2N}$ and ?? _M =1/2, while the typical fluctuations behave for large N like $M - \sqrt{2N} \propto s N^{-1/6}$ and ?? _M ?1/2??wN ^?1/3 where s and w are correlated random variables. One obtains an explicit expression of the limiting jpdf P(s,w) in terms of the Tracy-Widom distribution for the Gaussian Orthogonal Ensemble (GOE) of Random Matrix Theory and a psi-function for the Hastings-McLeod solution to the Painlevé II equation. Our result yields, up to a rescaling of the random variables s and w, an expression for the jpdf of the maximum and its position for the Airy₂ process minus a parabola. This latter describes the fluctuations in many different physical systems belonging to the Kardar-Parisi-Zhang (KPZ) universality class in 1+1 dimensions. In particular, the marginal probability density function (pdf) P(w) yields, up to a model dependent length scale, the distribution of the endpoint of the directed polymer in a random medium with one free end, at zero temperature. In the large w limit one shows the asymptotic behavior logP(w)???w ³/12.     

Nanosecond and femtosecond UV laser ablation of polymers: Influence of molecular weight

We examine the nanosecond and femtosecond UV laser ablation of poly(methyl methacrylate) (PMMA) as a function of molecular weight (M_w). For laser ablation with nanosecond laser pulses, at the excimer wavelengths 248 nm and 193 nm, we show that high temperatures develop; yet the dynamics of material ejection differs depending on polymer M_w. The results on the nanosecond ablation of polymers are accounted within the framework of bulk photothermal model and the results of molecular dynamics simulations. Turning next to the 248 nm ablation with 500 fs laser pulses, the ablation threshold and etching rates are also found to be dependent on polymer M_w. In addition, ablation results in morphological changes of the remaining substrate. Plausible mechanisms are advanced.     

The radiative corrections to the electroweak parameters in the dominant fermion-loop approximation

A simple treatment of the dominant radiative corrections to theW ^± andZ ⁰ mass formulae due to fermion-loop corrections to the propagator is given, including the possibility of a very massive top quark,m _t >M _w . A thorough comparison with the results of the complete (SU(2) _L ×U(1) _Y ) one-loop calculations is presented. Using α,G _μ andM _z as input, we find excellent agreement with the complete one-loop calculations (withm _HIGGS?100GeV) for all values ofm _t within an expected error ofΔM _W ?(α/2πM _W ?100MeV) inM _W andΔs _W ² ?0.002 in the weak angle,s _w ² . Technically we differ from previous work in diagonalizing the γZ propagator for arbitrary values ofq ², thus allowing for extensive use of the notion of “running” coupling constants and masses. We also give a simple and closed formula for the radiative corrections to be applied tos _w ² (accurate within an expected error ofΔs _w ² ?0.002), when extractings _W ² ?0.002), when extractings _W ² from neutrino scattering experiments. As a strategy for future precision tests of the electroweak theory, we suggest attempting to isolate and to test directly the “new physics” of boson loops and other new phenomena by comparing with and looking for deviations (larger thanΔM _W ?(α/2π)M _w ) from the predictions of the dominant fermion-loop calculation.     

How to compare the SU(5) value of sin2θw with experiments?

We establish the relation between κsin²θ_w to be found from neutral-current experiments and sin²θ_w(Q) for Q=M_W predicted by grand unified theories. We then calculate sin²θ_W(M_W) in the minimal SU(5) model taking the M_W as well as M_x threshold effects into account. We find that these two threshold effects on sin²θ_W(M_W) cancel with each other and sin²θ_W(M_W)=0.211± 0.005.     

On the self-consistency requirement in the low density expansion of the optical potential in nuclear matter

We critically discuss the choice of the auxiliary potential U which is introduced in the low density expansion of the mass operator M(k, w). This choice is related to the analytical properties of M(k, w) in the complex w-plane and we take due account of momentum conservation in the intermediate states appearing in the diagrams associated with M(k, w). We also provide a computation of the one-hole line, rearrangement and renormalization contributions to the optical potential, of the hole state spectral function and of the momentum distribution in nuclear matter. We use a real auxiliary potential which is self-consistent up to the order considered here, i.e. which takes into account the rearrangement and the renormalization corrections. Rearrangement is treated rigorously. The dependence of the obtained results on the choice of the nucleon-nucleon interaction, namely the Hamman-Ho Kim one in our calculation, is discussed.     

Heavy particles and the ϱ parameter in the standard model

A new formalism is presented for the calculation of the contribution δ? to ? = M_w²/M_z²cos²θ_w from heavy particles transforming according to arbitrary representations of SU(2) × U(1). A conjecture for the necessary and sufficient conditions that δ??0 for all values of masses and mixing angles within a particular multiplet is formulated. A number of examples are given (all consistent with the conjecture) and the significance of improved knowledge of ? vis à vis the possible existence of undiscovered heavy particles discussed.     

Identification of E6-generated Z′ from combined charm II,LEP 1, SLC high-precision measurements

We show that a combined analysis of three specific longitudinal polarization asymmetries in electron-positron annihilation on Z₀ resonance, of the mass ratio M_w/M_z and of the neutrino-electron neutral cross-section ratio, which could be measured in the near future at SLC, LEP, ACOL and CHARM II, would lead to a well-defined identification of a single new E₆-generated Z′. In particular, it might be possible to disentangle a superstring-inspired model from other currently considered possibilities down to values of the mixing angle θ_η = 0.02 and, at the same time, to fix the mass ratio ε = M_Z²/M_Z′² with known accuracy.     

Virtual very heavy top effects in LEP/SLC precision measurements

We estimate the O(α_s) strong interaction virtual corrections to the very heavy top (m_t = 200 GeV) virtual effects in several observable quantities to be measured in the near future in high precision experiments at LEP/SLC. In the cases of the measurements of M_w and of the longitudinal polarization asymmetry A_LR on Z₀ resonance we conclude that these corrections cannot be neglected, being of a size which is comparable with the effect coming from a possibly large Higgs mass, M_H≅1 TeV.     

Dynamically broken supergravity and the hierarchy problem

We propose a scenario for grand unified models based on local supersymmetry. We give arguments that condensates of strongly interacting gauge theories might break local supersymmetry. The gravitino mass induces mass splittings in the low energy theory and allows us to understand a hierarchy of M_p = 10¹⁹ GeV to M_w = 10² GeV naturally.     

Weinberg angle in the neutrino-electron scattering

According to my recent analysis, in which the use ofM _z has been found to give a more precise sin² θ _w than the use ofG _F inv _μ e→v _μ e scattering, I make calculations of sin² θ w in this process withM _z input including the full one-loop and all the leading log corrections. The result from the present data of cross-section σ(v _μ e) = (1.55±0.20)x10^?42 E _v andZ boson massM _z =92.6±1.7 GeV is sin² θ _w =0.228±0.016, which is in good agreement with the value 0.227±0.014 derived through the usual method from the data of \(v_\mu ,\bar v_\mu e\) and \(v_e ,\bar v_e e\) scatterings, and quite consistent with the world-average sin² θ w=0.228±0.004.     

Propagation properties of a non-paraxial hollow Gaussian beam

Based on the non-paraxial vectorial moment theory of beam propagation, the analytical expressions of the M² factors for a non-paraxial hollow Gaussian beam (HGB) have been derived. The analytical formulae are further simplified for paraxial and highly non-paraxial cases. The beam waists, the divergence angles and the beam propagation factors are also depicted as functions of the parameter w₀. The divergence angles will not exceed the maximum value of 90°. When w₀ is within the scale of one time of light wavelength, the TE polarization results in the different beam propagation factors in the two transverse directions and the beam propagation factors first increase and then decrease. When w₀ is large enough, the beam propagation factors are determined only by the beam order.     

Combined limits on the number of light neutrinos and the top mass from the measurement ofR=σ(W→ℓv)/σ(Z→ℓℓ)

Using the recent measurement of the ratio ofW→?v toZ→?? partial production cross-sections by UA1 and UA2, we derive an upper limit on the number of neutrinos and on the top quark mass, in the framework of the minimal standard model. To reduce the uncertainty on these limits, we use the most recent determination of sin² θ _w and the latest measurements of the structure functions by muon deep-inelastic experiments. No limit onm _top is obtained in the case of three neutrino families at the 95% C.L., while a fourth generation is excluded at this confidence level if the top mass is higher thanM _w ?m _b and if there is no new heavy lepton contribution in theW decay. The implications of light fourth generationb' andL are also investigated.     

Electroweak radiative corrections to neutrino and electron scattering and the value of sin2θw

We describe in detail the calculation of all first-order electroweak radiative corrections to total and differential neutrino cross sections and to the parity-violating asymmetry in ed scattering. We find that leading log approximations agree well with our exact result for the shape, but not necessarily the magnitude, of the corrections to $\text{d}\text{σ}{}^{\mathrm{<mtext>\nu ,</mtext><mtext>\nu </mtext>}}\text{/}\text{d}\text{γ}$ except for γ → 1. Corrections to total neutrino cross sections have also been calculated by Marciano and Sirlin; our results agree with theirs. The corrections to sin²θ_w are experiment dependent. If sin²θ_w is defined in the $\text{MS}$ scheme at a scale M_w, they reduce the average value found from the ratio of charged to neutral current neutrino scattering by 0.012 to 0.215 ± 0.015. They reduce the value obatained from the Paschos Wolfenstein relation by 0.008 to 0.221 ± 0.014. In ed scattering they reduce the value by 0.008 to 0.215 ± 0.015. Using a corrected value of 0.215 ± 0.015 and the first-order corrections to the mass formulae, the SU(2) × U(1) predictions for the vector boson masses are M_w = 83.1_?2.8^+3.1rmGeV and M_z = 93.8_?2.2^+2.5 GeV, about five GeV larger than obtained from the lowest order analysis.     

The beam quality of nonparaxial Hermite-sine-Gaussian beam

Based on the theory of the second intensity moment of nonparaxial scalar beam and the method of angular spectrum, the expressions for the far-field divergence angle, waist width and M² factor of nonparaxial Hermite-sine-Gaussian (HSiG) beams are derived. Calculation and analysis show the dependence of the far-field divergence angle of nonparaxial HSiG beams on the parameter w₀/λ, as well as on order m, And it with even and odd orders approach 73.898° and 63.435° as w₀/λ → 0. With increasing order m and the parameter w₀/λ, the waist width increase monotonously, which is same as paraxial case. But nonparaxial M² factor is different from paraxial case, it cannot only less than 1, but also approach 0 as w₀/λ → 0.     

Photon distribution functions of the fluorescence photons from a single nanoparticle in various photon counting methods

Simple expressions have been derived for three photon distribution functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) corresponding to three different methods for counting fluorescence photons from a single nanoparticle excited by continuous laser radiation. In contrast to the previously derived expressions represented in the form of N multiple integrals, the new expressions contain only single or double integrals of Poisson functions, which makes it possible to easily perform the numerical calculation of the photon distribution. The simplest photon counting method corresponds to the lengthiest function w _N ^M (T); on the contrary, the simplest function w _N ^O (T) corresponds to the most complex photon counting method. The functions w _N ^M (T), w _N ^Z (T), and w _N ^O (T) are noticeably different in short time intervals T; however, the distributions calculated using these functions are almost indistinguishable from each other in long T intervals. This circumstance makes it possible to use the simplest function w _N ^O (T) to consider the photon statistics measured by the simplest method. This possibility is particularly important for investigating the fluorescence photon statistics, where the intensity fluctuates.