Light bullets in quadratic media with normal dispersion at the second harmonic

Stable two- and three-dimensional spatiotemporal solitons (STSs) in second-harmonic-generating media are found in the case of normal dispersion at the second harmonic (SH). This result, surprising from the theoretical viewpoint, opens a way for experimental realization of STSs. An analytical estimate for the existence of STSs is derived, and full results, including a complete stability diagram, are obtained in a numerical form. STSs withstand not only the normal SH dispersion, but also finite walk-off between the harmonics, and readily self-trap from a Gaussian pulse launched at the fundamental frequency.Comment: 4 pages, 5 figures, accepted to Phys. Rev. Let

Critical thermodynamics of three-dimensional MN-component field model with cubic anisotropy from higher-loop \epsilon expansion

The critical thermodynamics of an $MN$-component field model with cubic anisotropy relevant to the phase transitions in certain crystals with complicated ordering is studied within the four-loop \ve expansion using the minimal subtraction scheme. Investigation of the global structure of RG flows for the physically significant cases M=2, N=2 and M=2, N=3 shows that the model has an anisotropic stable fixed point with new critical exponents. The critical dimensionality of the order parameter is proved to be equal to $N_c^C=1.445(20)$, that is exactly half its counterpart in the real hypercubic model.Comment: 9 pages, LaTeX, no figures. Published versio

Stable spinning optical solitons in three dimensions

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schrodinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.Comment: 4 pages, 6 figures, accepted to Phys. Rev. Let

Critical behavior of certain antiferromagnets with complicated ordering: Four-loop \ve-expansion analysis

The critical behavior of a complex N-component order parameter Ginzburg-Landau model with isotropic and cubic interactions describing antiferromagnetic and structural phase transitions in certain crystals with complicated ordering is studied in the framework of the four-loop renormalization group (RG) approach in (4-\ve) dimensions. By using dimensional regularization and the minimal subtraction scheme, the perturbative expansions for RG functions are deduced and resummed by the Borel-Leroy transformation combined with a conformal mapping. Investigation of the global structure of RG flows for the physically significant cases N=2 and N=3 shows that the model has an anisotropic stable fixed point governing the continuous phase transitions with new critical exponents. This is supported by the estimate of the critical dimensionality $N_c=1.445(20)$ obtained from six loops via the exact relation $N_c={1/2} n_c$ established for the complex and real hypercubic models.Comment: LaTeX, 16 pages, no figures. Expands on cond-mat/0109338 and includes detailed formula

A normal gem-dimethyl effect in the base-catalyzed cyclization of -( p-nitrophenyl)hydantoic acids: evidence for hindered proton transfer in the permethylated esters †

The cyclization of hydantoic acids 2-UA and 3-UA -kinetics, solvent kinetic isotope effects (SKIE) and buffer catalysis -were studied in an attempt to explain the disappearance of the gem-dimethyl effect (GDME) in the specific base-catalyzed cyclization of hydantoic esters. pH-Rate profiles for both acids (after correction for ionization and for reversibility at high pH) show two regions of unit slope corresponding to different mechanisms. For 2-UA at high pH and 3-UA at lower pH the mechanism is considered to involve rate-determining attack by the ureido anion on the neutral carboxy group, consistent with the observed inverse SKIE. The normal GDME of 15 provides strong evidence that anomalies observed with the esters do indeed result from steric hindrance to proton transfer. The change to rate determining departure of OH Ϫ with 2-UA is caused at low pH by acid catalysis of the reversion of the tetrahedral intermediate (T Ϫ ) to reactants, while with 3-UA at high pH this takes place through T 2Ϫ . The GDME favours attack on the carboxylate anion but makes ring opening more difficult, thus decreasing acid inhibition. The observed β = 0.44 for general base catalysis of the cyclization of 2-UA is consistent with concerted deprotonation and attack of the ureido group. With 3-UA two simultaneous general base-catalyzed reactions take place: slow deprotonation of the ureido group (β = 1.0) and attack of the ureide anion on the carboxy anion aided by the buffer conjugate acid. The estimated GDME is 2800 for the equilibrium between acid anion and hydantoin, ‡ but only 45 and 15 for catalysis by H 3 O ϩ and OH Ϫ , respectively: both reactions are presumed to go through early transition states. A convenient way to accelerate the bioorganic reactions of small molecules is to introduce steric strain into the substrate. In cyclization reactions this is readily done by introducing substituents into the interconnecting chain: the resulting increase in rate defines the gem-dimethyl effect (GDME). 1 However, in a recent study 2,3 of catalytic mechanisms for the ring closure of hydantoic esters, we found no GDME for the base-catalyzed reaction. We concluded that the rate determining step had changed, for the most heavily substituted compounds, from the formation of the tetrahedral intermediate to its breakdown, because of steric hindrance in proton transfer to the leaving ethoxy group. In the tetrahedral intermediate, T Ϫ , the two methyl groups screen one side and the N-aryl substituent the other, while R (ethyl was studied) in its least hindered conformation blocks easy access of a general acid. If this analysis is correct, and the effect depends on steric hindrance in proton † Pseudo-first-order rate constants are available as supplementary data. For direct electronic access see http://www.rsc.org/suppdata/p2/b0/ b002276o ‡ The IUPAC name for hydantoin is imidazolidine-2,4-dione. transfer to the developing ethoxide by its ethyl group, it should be reduced or removed if a smaller group replaces ethyl. We have tested this proposition by studying the cyclization of the hydantoic acids shown in Scheme 1. We find that hydantoic acids 2 and 3 undergo base-catalyzed ring closure more slowly than the esters when the pH is higher than the pK of the COOH group; and that the results confirm our prediction. The hydroxide-catalyzed cyclization of the fully methylated acid 3-UA shows a normal GDME, and the solvent kinetic isotope effects (SKIE) suggest that acids 2-UA and 3-UA are cyclized by the same mechanism. Experimental Materials Inorganic reagents and buffer components were of analytical Scheme

Three-loop renormalization group analysis of a complex model with stable fixed point: Critical exponents up to ϵ3\epsilon^3 and ϵ4\epsilon^4

The complete analysis of a model with three quartic coupling constants associated with an O(2N)--symmetric, a cubic, and a tetragonal interactions is carried out within the three-loop approximation of the renormalization-group (RG) approach in $D=4-2\epsilon$ dimensions. Perturbation expansions for RG functions are calculated using dimensional regularization and the minimal subtraction (MS) scheme. It is shown that for $N\ge 2$ the model does possess a stable fixed point in three dimensional space of coupling constants, in accordance with predictions made earlier on the base of the lower-order approximations. Numerical estimate for critical (marginal) value of the order parameter dimensionality $N_c$ is given using Pad\'e-Borel summation of the corresponding $\epsilon$--expansion series obtained. It is observed that two-fold degeneracy of the eigenvalue exponents in the one-loop approximation for the unique stable fixed point leads to the substantial decrease of the accuracy expected within three loops and may cause powers of $\sqrt{\epsilon}$ to appear in the expansions. The critical exponents $\gamma$ and $\eta$ are calculated for all fixed points up to $\epsilon^3$ and $\epsilon^4$, respectively, and processed by the Borel summation method modified with a conformal mapping. For the unique stable fixed point the magnetic susceptibility exponent $\gamma$ for N=2 is found to differ in third order in $\epsilon$ from that of an O(4)--symmetric point. Qualitative comparison of the results given by $\epsilon$--expansion, three-dimensional RG analysis, non-perturbative RG arguments, and experimental data is performed.Comment: 30 pages, LaTeX, no figures. To be published in Phys. Rev. B, V.57, Jan. issue (1998

Experimental and numerical analysis of initial plasticity in P91 steel small punch creep samples

To date, the complex behaviour of small punch creep test (SPCT) specimens has not been completely understood, making the test hard to numerically model and the data difficult to interpret. This paper presents a novel numerical model able to generate results that match the experimental findings. For the first time, pre-strained uniaxial creep test data of a P91 steel at 600 °C have been implemented in a conveniently modified Liu and Murakami creep damage model in order to simulate the effects of the initial localised plasticity on the subsequent creep response of a small punch creep test specimen. Finite element (FE) results, in terms of creep displacement rate and time to failure, obtained by the modified Liu and Murakami model are in good agreement with experimental small punch creep test data. The rupture times obtained by the FE calculations which make use of the non-modified creep damage model are one order of magnitude shorter than those obtained by using the modified constitutive model. Although further investigation is needed, this novel approach has confirmed that the effects of initial localised plasticity, taking place in the early stages of small punch creep test, cannot be neglected. The new results, obtained by using the modified constitutive model, show a significant improvement with respect to those obtained by a state of the art creep damage constitutive model (the Liu and Murakami constitutive model) both in terms of minimum load-line displacement rate and time to rupture. The new modelling method will potentially lead to improved capability for SPCT data interpretatio

An overview of using small punch testing for mechanical characterization of MCrAlY bond coats

Considerable work has been carried out on overlay bond coats in the past several decades because of its excellent oxidation resistance and good adhesion between the top coat and superalloy substrate in the thermal barrier coating systems. Previous studies mainly focus on oxidation and diffusion behavior of these coatings. However, the mechanical behavior and the dominant fracture and deformation mechanisms of the overlay bond coats at different temperatures are still under investigation. Direct comparison between individual studies has not yet been achieved due to the fragmentary data on deposition processes, microstructure and, more apparently, the difficulty in accurately measuring the mechanical properties of thin coatings. One of the miniaturized specimen testing methods, small punch testing, appears to have the potential to provide such mechanical property measurements for thin coatings. The purpose of this paper is to give an overview of using small punch testing to evaluate material properties and to summarize the available mechanical properties that include the ductile-to-brittle transition and creep of MCrAlY bond coat alloys, in an attempt to understand the mechanical behavior of MCrAlY coatings over a broad temperature range

Of the importance of a leaf: the ethnobotany of sarma in Turkey and the Balkans

BACKGROUND: Sarma - cooked leaves rolled around a filling made from rice and/or minced meat, possibly vegetables and seasoning plants - represents one of the most widespread feasting dishes of the Middle Eastern and South-Eastern European cuisines. Although cabbage and grape vine sarma is well-known worldwide, the use of alternative plant leaves remains largely unexplored. The aim of this research was to document all of the botanical taxa whose leaves are used for preparing sarma in the folk cuisines of Turkey and the Balkans. Methods: Field studies were conducted during broader ethnobotanical surveys, as well as during ad-hoc investigations between the years 2011 and 2014 that included diverse rural communities in Croatia, Bosnia and Herzegovina, Serbia, Kosovo, Albania, Macedonia, Bulgaria, Romania, and Turkey. Primary ethnobotanical and folkloric literatures in each country were also considered. Results: Eighty-seven botanical taxa, mainly wild, belonging to 50 genera and 27 families, were found to represent the bio-cultural heritage of sarma in Turkey and the Balkans. The greatest plant biodiversity in sarma was found in Turkey and, to less extent, in Bulgaria and Romania. The most commonly used leaves for preparing sarma were those of cabbage (both fresh and lacto-fermented), grape vine, beet, dock, sorrel, horseradish, lime tree, bean, and spinach. In a few cases, the leaves of endemic species (Centaurea haradjianii, Rumex gracilescens, and R. olympicus in Turkey) were recorded. Other uncommon sarma preparations were based on lightly toxic taxa, such as potato leaves in NE Albania, leaves of Arum, Convolvulus, and Smilax species in Turkey, of Phytolacca americana in Macedonia, and of Tussilago farfara in diverse countries. Moreover, the use of leaves of the introduced species Reynoutria japonica in Romania, Colocasia esculenta in Turkey, and Phytolacca americana in Macedonia shows the dynamic nature of folk cuisines. Conclusion: The rich ethnobotanical diversity of sarma confirms the urgent need to record folk culinary plant knowledge. The results presented here can be implemented into initiatives aimed at re-evaluating folk cuisines and niche food markets based on local neglected ingredients, and possibly also to foster trajectories of the avant-garde cuisines inspired by ethnobotanical knowledge