The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic

Continuous dependence results for Non-linear Neumann type boundary value problems

We obtain estimates on the continuous dependence on the coefficient for second order non-linear degenerate Neumann type boundary value problems. Our results extend previous work of Cockburn et.al., Jakobsen-Karlsen, and Gripenberg to problems with more general boundary conditions and domains. A new feature here is that we account for the dependence on the boundary conditions. As one application of our continuous dependence results, we derive for the first time the rate of convergence for the vanishing viscosity method for such problems. We also derive new explicit continuous dependence on the coefficients results for problems involving Bellman-Isaacs equations and certain quasilinear equation

On the L_p-solvability of higher order parabolic and elliptic systems with BMO coefficients

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be merely measurable in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. For the proof, we develop a set of new techniques to produce mean oscillation estimates for systems on a half space.Comment: 44 pages, introduction revised, references expanded. To appear in Arch. Rational Mech. Ana

No classical limit of quantum decay for broad states

Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow states. The non exponential nature at large times is however hard to establish from experiments. A method to recover the time evolution of unstable states from a parametrization of the amplitude fitted to data is presented. We apply the method to a realistic example of a very broad state, the sigma meson and reveal that an exponential decay is not a valid approximation at any time for this state. This example derived from experiment, shows the unique nature of broad resonances

New approach to (quasi)-exactly solvable Schrodinger equations with a position-dependent effective mass

By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schr\"odinger equation with a position-dependent effective mass. In the latter case, SUSYQM techniques provide us with some additional new potentials.Comment: 11 pages, no figur

Complex Scaled Spectrum Completeness for Coupled Channels

The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case of inelastic scattering with many channels, the existence of such a resolution under complex scaling is still debated. Taking advantage of results obtained earlier for the two channel case, this paper proposes a representation in which the convergence of a resolution of the identity can be more easily tested. The representation is valid for any finite number of coupled channels for inelastic scattering without rearrangement.Comment: Latex file, 13 pages, 4 eps-figure

МИКРОЭКСТРАКЦИОННОЕ ФЛОТАЦИОННОЕ КОНЦЕНТРИРОВАНИЕ И ОПРЕДЕЛЕНИЕ ХЛОРУКСУСНЫХ КИСЛОТ В ВОДЕ

The flotation-assisted liquid-liquid microextraction method of mono-, di -, and trichloroacetic acids (CAAs) has been developed. Methyl tert-butyl ether (MTBE) was used as an extractant. The emulsification was performed by the ultrasonic irradiation. The microextraction procedure was carried out in a 27 ml special tube. It was equipped with the capillaries for sampling the extract and an air outlet. A salting-out additive (Na2SO4) was used to reduce the solubility of MTBE in water and to increase the extraction efficiency of CAAs. The air passage through the emulsion of the extractant was carried out using the eight-channel capillary bubbler. The organic matrix replacement was applied for ion chromatographic determination of CAAs with the conductivity detection. Current study showed the advantages of the flotation-assisted demulsification over the centrifugal one. The concentration factors of chlorinated acetic acids were 2-3 times higher. The detection limits of CAAs in water were reduced to (5·10-4 - 4·10-3 mg/l). The extraction time was reduced by more than three times. The trueness of the determination of HUC impurities was confirmed by the addition method. The statistical insignificance of the systematic error in comparison with the random error was shown. The developed method of preconcentration in combination with ion chromatography made it possible to determine the concentrations of CAAs 40-1250 times lower than the normalized SanPiN and WHO. This allowed conducting a highly sensitive determination of CAAs in water long before the onset of the critical ecological state.Keywords: chlorinated acetic acids, ion chromatography, liquid-liquid microextraction, flotation-assisted demulsificationDOI: http://dx.doi.org/10.15826/analitika.2021.25.2.002 V.A. Krylov, R.G. Mosyagin  Lobachevsky State University of Nizhny Novgorod (UNN)Gagarin pr., 23, Nizhny Novgorod, 603950, Russian FederationПредложен метод флотационного выделения экстракта при дисперсионном жидкостно-жидкостном микроэкстракционном концентрировании (ДЖЖМЭ) моно-, ди- и трихлоруксусных кислот (ХУК). В качестве экстрагента использован метил-трет-бутиловый эфир (МТБЭ), его эмульгирование осуществляли с помощью ультразвукового воздействия. Концентрирование проводили в ампуле объемом 27 мл, которая оснащена капиллярами для отбора микроколичеств экстракта и отводом для барботирования воздуха. Пропускание воздуха через эмульсию экстрагента осуществлено с применением восьмиканального капиллярного барботера. Для уменьшения растворимости МТБЭ в воде и повышения эффективности концентрирования ХУК использовали высаливающую добавку (Na2SO4). Для ионохроматографического определения ХУК проводили замену органической матрицы экстракта на водную. Показаны преимущества флотационного способа деэмульсификации перед центрифужным: достигнуты коэффициенты концентрирования хлоруксусных кислот в 2-3 раз большие, а пределы обнаружения ХУК в воде понижены до 5·10-4 − 4·10-3 мг/л, время выделения экстракта уменьшено более чем в три раза. Правильность определения примесей ХУК в воде подтверждена методом добавок. Показана  статистическая незначимость систематической погрешности по сравнению со случайной. Разработанная методика концентрирования в сочетании с ионной хроматографией позволяет определять концентрации ХУК в 40-1250 раз меньшие, чем нормированные СанПиН и ВОЗ. Это дает возможность проводить высокочувствительное определение ХУК в воде задолго до наступления критических экологических  состояний.Ключевые слова: хлоруксусные кислоты, ионная хроматография, микроэкстракционное концентрирование, флотационная деэмульсификацияDOI: http://dx.doi.org/10.15826/analitika.2021.25.2.00

Comment on ``Lyapunov Exponent of a Many Body System and Its Transport Coefficients''

In a recent Letter, Barnett, Tajima, Nishihara, Ueshima and Furukawa obtained a theoretical expression for the maximum Lyapunov exponent $\lambda_1$ of a dilute gas. They conclude that $\lambda_1$ is proportional to the cube root of the self-diffusion coefficient $D$, independent of the range of the interaction potential. They validate their conjecture with numerical data for a dense one-component plasma, a system with long-range forces. We claim that their result is highly non-generic. We show in the following that it does not apply to a gas of hard spheres, neither in the dilute nor in the dense phase.Comment: 1 page, Revtex - 1 PS Figs - Submitted to Physical Review Letter

Largest Lyapunov Exponent for Many Particle Systems at Low Densities

The largest Lyapunov exponent $\lambda^+$ for a dilute gas with short range interactions in equilibrium is studied by a mapping to a clock model, in which every particle carries a watch, with a discrete time that is advanced at collisions. This model has a propagating front solution with a speed that determines $\lambda^+$, for which we find a density dependence as predicted by Krylov, but with a larger prefactor. Simulations for the clock model and for hard sphere and hard disk systems confirm these results and are in excellent mutual agreement. They show a slow convergence of $\lambda^+$ with increasing particle number, in good agreement with a prediction by Brunet and Derrida.Comment: 4 pages, RevTeX, 2 Figures (encapsulated postscript). Submitted to Phys. Rev. Let