Morphology and scaling in the noisy Burgers equation: Soliton approach to the strong coupling fixed point

The morphology and scaling properties of the noisy Burgers equation in one dimension are treated by means of a nonlinear soliton approach based on the Martin-Siggia-Rose technique. In a canonical formulation the strong coupling fixed point is accessed by means of a principle of least action in the asymptotic nonperturbative weak noise limit. The strong coupling scaling behaviour and the growth morphology are described by a gas of nonlinear soliton modes with a gapless dispersion law and a superposed gas of linear diffusive modes with a gap. The dynamic exponent is determined by the gapless soliton dispersion law, whereas the roughness exponent and a heuristic expression for the scaling function are given by the form factor in a spectral representation of the interface slope correlation function. The scaling function has the form of a Levy flight distribution.Comment: 5 pages, Revtex file, submitted to Phys. Rev. Let

Fractional Operators, Dirichlet Averages, and Splines

Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose of this paper to show that there are deep and interesting relationships between these three areas. First a brief introduction to fractional differential and integral operators defined on Lizorkin spaces is presented and some of their main properties exhibited. This particular approach has the advantage that several definitions of fractional derivatives and integrals coincide. We then introduce Dirichlet averages and extend their definition to an infinite-dimensional setting that is needed to exhibit the relationships to splines of complex order. Finally, we focus on splines of complex order and, in particular, on cardinal B-splines of complex order. The fundamental connections to fractional derivatives and integrals as well as Dirichlet averages are presented

The Detection of Outflows in the IR-Quiet Molecular Core NGC 6334 I(North)

We find strong evidence for outflows originating in the dense molecular core NGC 6334 I(North): a 1000 Msol molecular core distinguished by its lack of HII regions and mid-IR emission. New observations were obtained of the SiO 2-1 and 5-4 lines with the SEST 15-m telescope and the H2 (1-0) S(1) line with the ESO 2.2-m telescope. The line profiles of the SiO transitions show broad wings extending from -50 to 40 km/s, and spatial maps of the line wing emission exhibit a bipolar morphology with the peaks of the red and blue wing separated by 30". The estimated mass loss rate of the outflow is comparable to those for young intermediate to high-mass stars. The near-IR images show eight knots of H2 emission. Five of the knots form a linear chain which is displaced from the axis of the SiO outflow; these knots may trace shock excited gas along the path of a second, highly collimated outflow. We propose that I(N) is a rare example of a molecular core in an early stage of cluster formation.Comment: 4 pages, LaTeX, 3 ps figures, accepted by ApJ

Asymmetric Thermal Lineshape Broadening in a Gapped 3-Dimensional Antiferromagnet - Evidence for Strong Correlations at Finite Temperature

It is widely believed that magnetic excitations become increasingly incoherent as temperature is raised due to random collisions which limit their lifetime. This picture is based on spin-wave calculations for gapless magnets in 2 and 3 dimensions and is observed experimentally as a symmetric Lorentzian broadening in energy. Here, we investigate a three-dimensional dimer antiferromagnet and find unexpectedly that the broadening is asymmetric - indicating that far from thermal decoherence, the excitations behave collectively like a strongly correlated gas. This result suggests that a temperature activated coherent state of quasi-particles is not confined to special cases like the highly dimerized spin-1/2 chain but is found generally in dimerized antiferromagnets of all dimensionalities and perhaps gapped magnets in general

Radiosurgery for the control of glomus jugulare tumours

Objective: To ascertain the efficacy of stereotactic radiosurgery (gamma knife) for the control of glomus jugulare tumours.Method: Between March 1994 and December 1997 we treated eight patients of glomus jugulare tumour with radiosurgery. These patients have been followed for more than four years (range 52 to 97 months). The age of the patients ranged between 32-64 years (mean 53 years). The male: female ratio was 3:5. Three patients had previously undergone surgery and one had unsuccessful embolization. The dose applied to tumour margin ranged between 16-25 Gy (median 25 Gy). Patients were followed up with yearly MRI scans and where possible with cerebral angiography.Results: All patients showed stabilisation of their symptoms following radiosurgery and six improved clinically. Five of these patients showed decrease in the size of lesion seen objectively on radiology, either slight to moderate decrease seen on the MRI scan or reduction in size and vascularity seen on cerebral angiography. The procedure is minimally invasive and none of the patients showed any adverse effect to radiosurgery.Conclusion: These results are encouraging but because of its naturally slow growth rate, up to 10 years of follow up will be necessary to establish a cure rate after radiosurgery for these lesions

Ordered Level Planarity, Geodesic Planarity and Bi-Monotonicity

We introduce and study the problem Ordered Level Planarity which asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a y-monotone curve. This can be interpreted as a variant of Level Planarity in which the vertices on each level appear in a prescribed total order. We establish a complexity dichotomy with respect to both the maximum degree and the level-width, that is, the maximum number of vertices that share a level. Our study of Ordered Level Planarity is motivated by connections to several other graph drawing problems. Geodesic Planarity asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a polygonal path composed of line segments with two adjacent directions from a given set $S$ of directions symmetric with respect to the origin. Our results on Ordered Level Planarity imply $NP$-hardness for any $S$ with $|S|\ge 4$ even if the given graph is a matching. Katz, Krug, Rutter and Wolff claimed that for matchings Manhattan Geodesic Planarity, the case where $S$ contains precisely the horizontal and vertical directions, can be solved in polynomial time [GD'09]. Our results imply that this is incorrect unless $P=NP$. Our reduction extends to settle the complexity of the Bi-Monotonicity problem, which was proposed by Fulek, Pelsmajer, Schaefer and \v{S}tefankovi\v{c}. Ordered Level Planarity turns out to be a special case of T-Level Planarity, Clustered Level Planarity and Constrained Level Planarity. Thus, our results strengthen previous hardness results. In particular, our reduction to Clustered Level Planarity generates instances with only two non-trivial clusters. This answers a question posed by Angelini, Da Lozzo, Di Battista, Frati and Roselli.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Hydrodynamic approach to coherent nuclear spin transport

We develop a linear response formalism for nuclear spin diffusion in a dipolar coupled solid. The theory applies to the high-temperature, long-wavelength regime studied in the recent experiments of Boutis et al. [Phys. Rev. Lett. 92, 137201 (2004)], which provided direct measurement of interspin energy diffusion in such a system. A systematic expansion of Kubo's formula in the flip-flop term of the Hamiltonian is used to calculate the diffusion coefficients. We show that this approach is equivalent to the method of Lowe and Gade [Phys. Rev. 156, 817 (1967)] and Kaplan [Phys. Rev. B 2, 4578 (1970)], but has several calculational and conceptual advantages. Although the lowest orders in this expansion agree with the experimental results for magnetization diffusion, this is not the case for energy diffusion. Possible reasons for this disparity are suggested.Comment: 7 pages, REVTeX4; Published Versio

Impact of an improved radiation scheme in the MAECHAM5 General Circulation Model

In order to improve the representation of the shortwave radiative transfer in the MAECHAM5 general circulation model, the spectral resolution of the shortwave radiation parameterization used in the model has been increased and extended in the UV-B and UV-C bands. The upgraded shortwave parameterization is first validated offline with a 4 stream discrete-ordinate line-by-line model. Thereafter, two 20-years simulations with the MAECHAM5 middle atmosphere general circulation model are performed to evaluate the temperature changes and the dynamical feedbacks arising from the newly introduced parameterization. The offline clear-sky comparison of the standard and upgraded parameterizations with the discrete ordinate model shows considerable improvement for the upgraded parameterization in terms of shortwave fluxes and heating rates. In the simulation with the upgraded ratiation parameterization, we report a significant warming of almost the entire atmosphere, largest at 1 hPa at the stratopause, and stronger zonal mean zonal winds in the middle atmosphere. The warming at the summer stratopause alleviates the cold bias present in the model when the standard radiation scheme is used. The stronger zonal mean zonal winds induce a dynamical feedback that results in a dynamical warming (cooling) of the polar winter (summer) mesosphere, caused by an increased downward (upward)circulation in the winter (summer) hemisphere. In the troposphere, the changes in the spectral resolution and the associated changes in the cloud optical parameters introduce a relatively small warming and, consistenly, a moisteneing. The warming occurs mostly in the upper troposphere and can contribute to a possible improvement of the model temperature climatology

Heteropolyacids supported on zirconia-doped γ, θ and α alumina: A physicochemical assessment and characterisation of supported solid acids

In this paper we carry out a surface study of promising supported solid acid catalysts commonly used for the production of high value chemicals derived from glycerol. In particular, γ, θ and α alumina (Al2O3) were modified by (i) grafting with 5 wt% zirconia, (ii) doping with 30 wt% silicotungstic acid (STA), and (iii) using both zirconia and STA. The aim is to rationalise the effect of these different parameters on structural properties and surface adsorption through a comprehensive multi-technique approach, including recently developed NMR relaxation techniques. XRD and laser Raman spectroscopy confirmed a strong interaction between STA and the γ-/θ-Al2O3 resulting in a distortion of the supported STA Keggin structure relative to that of bulk STA. Conversely, a much weaker interaction between the supported STA and α-Al2O3 was measured. NMR relaxation demonstrated that the STA doping increases the adsorption properties of the catalyst, particularly for γ-/θ-Al2O3. For catalysts based on α-Al2O3, such effect was negligible. Thermogravimetric/differential thermogravimetry (TGA/DTG) analysis suggested that zirconia-grafted and non-grafted θ-Al2O3 and γ-Al2O3 are suitable materials for increasing the thermal stability of STA whereas α-Al2O3 (both grafted and non-grafted) does not improve the thermal stability of STA