Potential Energy Difference Research Articles

Effect of Metal Doping and Vacancies on the Thermal Conductivity of Monolayer Molybdenum Diselenide.

It is well understood that defect engineering can give rise to exotic electronic properties in transition-metal dichalcogenides, but to this date, there is no detailed study to illustrate how defects can be engineered to tailor their thermal properties. Here, through combined experimental and theoretical approaches based on the first-principles density functional theory and Boltzmann transport equations, we have explored the effect of lattice vacancies and substitutional tungsten (W) doping on the thermal transport of the suspended molybdenum diselenide (MoSe2) monolayers grown by chemical vapor deposition (CVD). The results show that even though the isoelectronic substitution of the W atoms for Mo atoms in CVD-grown Mo0.82W018Se2 monolayers reduces the Se vacancy concentration by 50% compared to that found in the MoSe2 monolayers, the thermal conductivity remains intact in a wide temperature range. On the other hand, Se vacancies have a detrimental effect for both samples and more so in the Mo0.82W018Se2 monolayers, which results in thermal conductivity reduction up to 72% for a vacancy concentration of 4%. This is because the mass of the W atom is larger than that of the Mo atom, and missing a Se atom at a vacancy site results in a larger mass difference and therefore kinetic energy and potential energy difference. Furthermore, the monotonically increasing thermal conductivity with temperature for both systems at low temperatures indicates the importance of boundary scattering over defects and phonon-phonon scattering at these temperatures.

Ядерный квадрупольный резонанс в кристаллах с неравноямным реориентационным движением

Effect of the reorientation motion of molecules and separate molecular fragments occurring between the positions with unequal potential energy, on the NQR frequency and the time T 1 of the spin-lattice relaxation of chemically and crystallographically nonequivalent resonant nuclei directly participating in the reorientational motion are considered. In the temperature dependences of these parameters, the following characteristic features are observed: the reorientational fade out temperatures of the resonant signals for nonequivalent nuclei can vary significantly; exponential (reorientational) parts of dependencies log T 1 vs 1/ T of these nuclei are parallel; the spin-lattice relaxation times caused by the reorientation mechanism become substantially longer. We discuss a qualitative relation of these features with the potential energy difference between the orientation positions on the one hand and with the angle between the rotation axis and the direction of the electric field gradient for nonequivalent quadrupole nuclei on the other hand.

Structure and Capacitance of Electrical Double Layers at the Graphene–Ionic Liquid Interface

Molecular dynamics simulations are carried out to investigate the structure and capacitance of the electrical double layers (EDLs) at the interface of vertically oriented graphene and ionic liquids [EMIM]+/[BF4]−. The distribution and migration of the ions in the EDL on the rough and non-rough electrode surfaces with different charge densities are compared and analyzed, and the effect of the electrode surface morphology on the capacitance of the EDL is clarified. The results suggest that alternate distributions of anions and cations in several consecutive layers are formed in the EDL on the electrode surface. When the electrode is charged, the layers of [BF4]− anions experience more significant migration than those of [EMIM]+ cations. These ion layers can be extended deeper into the bulk electrolyte solution by the stronger interaction of the rough electrode, compared to those on the non-rough electrode surface. The potential energy valley of ions on the neutral electrode surface establishes a potential energy difference to compensate the energy cost of the ion accumulation, and is capable of producing a potential drop across the EDL on the uncharged electrode surface. Due to the greater effective contact area between the ions and electrode, the rough electrode possesses a larger capacitance than the non-rough one. In addition, it is harder for the larger-sized [EMIM]+ cations to accumulate in the narrow grooves on the rough electrode, when compared with the smaller [BF4]−. Consequently, the double-hump-shaped C–V curve (which demonstrates the relationship between differential capacitance and potential drop across the EDL) for the rough electrode is asymmetric, where the capacitance increases more significantly when the electrode is positively charged.

The Impact of Layer Perturbation Potential Energy on the East Asian Summer Monsoon

This paper analyzes the relationship between the 1000–850-hPa layer perturbation potential energy (LPPE) as the difference in local potential energy between the actual state and the reference state and the East Asian summer monsoon (EASM) using reanalysis and observational datasets. The EASM is closely related to the first-order moment term of LPPE (LPPE1) from the preceding March to the boreal summer over three key regions: the eastern Indian Ocean, the subtropical central Pacific, and midlatitude East Asia. The LPPE1 pattern (−, +, +), with negative values over the eastern Indian Ocean, positive values over the subtropical central Pacific, and positive values over East Asia, corresponds to negative LPPE1 anomalies over the south of the EASM region but positive LPPE1 anomalies over the north of the EASM region, which lead to an anomalous downward branch over the southern region but an upward branch over the northern region. The anomalous vertical motion affects the local meridional circulation over East Asia that leads to a southwesterly wind anomaly over East Asia (south of 30°N) at 850 hPa and anomalous downward motion over 100°–120°E (along 25°–35°N), resulting in a stronger EASM, more kinetic energy over the EASM region, and less boreal summer rainfall in the middle and lower reaches of the Yangtze River valley (24°–36°N, 90°–125°E). These LPPE1 anomalies in the eastern Indian Ocean and subtropical central Pacific appear to be connected to changes in local sea surface temperature through the release of latent heat.

Three sources of errors in the Ehrenfest treatment of inelastic scattering and possible ways of resolving them.

In order to identify the origin of possible errors in the mixed quantum/classical approach to inelastic scattering [A. Semenov and D. Babikov, J. Chem. Phys. 140, 044306 (2014) and A. Semenov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 141, 114304 (2014)], a simplified model is considered that consists of one intermolecular degree of freedom and two intramolecular states, coupled by a simple potential. For this system, analytic derivations are carried out to determine (i) the exact quantum mechanical solution of the inelastic scattering problem, (ii) a simplified version of it with all oscillatory terms neglected, and (iii) the Ehrenfest solution in which the translational motion is described by the mean-field trajectory while the internal molecular motion is treated by the time-dependent Schrodinger equation. It is shown that the appropriate choice of velocity for the mean-field trajectory permits to enforce microscopic reversibility and gives results in excellent agreement with full-quantum results. The average velocity method of Billing is rigorously derived as a limiting case (of this more general approach), when reversibility is enforced locally, at the initial moment of time only. It is demonstrated that errors of state-to-state transition probabilities in the Ehrenfest approach occur at lower values of total energy E if the magnitudes of excitation energy ΔE, potential energy difference between the two states ΔV, and coupling of two states V12 are large. Possible ways of applying this concept to rotational transitions in real molecules are explored, using examples from CO + CO inelastic scattering.

A novel mutation in homeobox DNA binding domain of HOXC13 gene underlies pure hair and nail ectodermal dysplasia (ECTD9) in a Pakistani family

BackgroundPure hair and nail ectodermal dysplasia (PHNED) is a congenital disorder of hair abnormalities and nail dysplasia. Both autosomal recessive and dominant inheritance fashion of PHNED occurs. In literature, to date, five different forms of PHNED have been reported at molecular level, having three genes known and two loci with no gene yet.MethodsIn this study, a four generations consanguineous family of Pakistani origin with autosomal recessive PHNED was investigated. Affected members exhibited PHNED phenotypes with involvement of complete hair loss and nail dysplasia. To screen for mutation in the genes (HOXC13, KRT74, KRT85), its coding exons and exons-intron boundaries were sequenced. The 3D models of normal and mutated HOXC13 were predicted by using homology modeling.ResultsThrough investigating the family to known loci, the family was mapped to ectodermal dysplasia 9 (ECTD9) loci with genetic address of 12q13.13. Mutation screening revealed a novel missense mutation (c.929A > C; p.Asn310Thr) in homeobox DNA binding domain of HOXC13 gene in affected members of the family. Due to mutation, loss of hydrogen bonding and difference in potential energy occurs, which may resulting in alteration of protein function.ConclusionThis is the first mutation reported in homeodomain, while 5th mutation reported in HOXC13 gene causing PHNED.

Up-Hill Diffusion of Phase-Separated FeCu Melt by Molecular Dynamics Simulation**Supported by the National Natural Science Foundation of China under Grant No 51371108, 51501104 and 51501103.

Molecular dynamics simulation is performed to characterize the concentration fluctuation of FeCu melts during the liquid–liquid phase separation process, which undergoes the following stages: the formation of interconnected structure and its coarsening, migration and coagulation of droplets driven by the decreasing of potential energy. The up-hill diffusion happens at the early relaxation period in which Cu atoms in Fe-rich region are forced to move toward Cu-rich region by spinodal decomposition with 90% Cu content in Cu-rich region and 95% Fe content in Fe-rich region at temperature of 1500 K. The higher diffusion rate of homogeneous atom can be observed at lower temperature, which is attributed to the larger potential energy difference between Cu-rich region and Fe-rich region. It also exhibits energy heterogeneity in the separated liquid. The domain size decreases sharply during the aggregation and coarsening of droplets, after that it keeps unchanged until the coagulation of droplets begins. The studies characterize concentration and energy heterogeneity of phase-separated liquid on the atomic scale.

Combined approach using capillary electrophoresis, NMR and molecular modeling for ambrisentan related substances analysis: Investigation of intermolecular affinities, complexation and separation mechanism

A comprehensive investigation on the CE separation mechanisms and on the inclusion complexation with CyDs of the chiral drug S-ambrisentan (S-AMB), its R-enantiomer and other impurities was performed by different techniques. A CE method was previously set up allowing the simultaneous determination of the enantiomeric purity and of impurities of S-AMB, based on the addition of SDS micelles and γ-cyclodextrin (γCyD) to borate buffer. In this study, the electrophoretic behavior of the analytes in terms of selectivity and mobility with respect to the addition of different CyDs was first investigated, evidencing the presence of interactions for all the CyDs, but the unique ability of γCyD for obtaining the separation of all the compounds. By molecular modeling, aggregates between SDS micelles and analytes, and inclusion complexes between CyDs, SDS and/or analytes of different stoichiometries were simulated. The potential and the gain energy of complexes were calculated on the minimized conformations, showing the great tendency of γCyD of forming mixed complexes with one or two SDS molecules and with the analyte, even if with different affinities among the analytes. For 1:1:1 mixed complexes with different CyDs, the highest difference of potential energy between the enantiomers’ complexes was observed for γCyD. Two-dimensional NOE spectroscopy experiments were performed for S-AMB and I1 and pointed out the interactions of the aromatic moiety of the analytes and of SDS aliphatic chain with γCyD protons, confirming the existence of γCyD mixed complexes. The high affinity of SDS for the γCyD cavity was suggested to justify the fundamental role of SDS in modulating and achieving the CE separation, due to its influence both on the stability and on the type of complexes between γCyD and the analytes.

Understanding the Role of Water in 1,10-Phenanthroline Monohydrate.

The solid forms emerging from an experimental screening programme of 1,10-phenanthroline (o-phen), a heavily used bidentate ligand, and interconversion pathways of its two neat forms, the monohdyrate (Hy1) and four solvates with acetone, chloroform, dichloromethane and 1,2-dichloroethane are described. The solvates, identified and characterised with thermoanalyical methods, are unstable when removed from the mother liquor and desolvate at room temperature depending on the relative humidity (RH) to anhydrate I° (AH I°) or transform to Hy1. At ambient conditions Hy1, a stoichiometric channel hydrate, is the thermodynaically most stable o-phen solid form. The enthalpically stabilised Hy1 melts at 102 °C or dehydrates to AH I° at RH < 10% at 25 °C. The potential energy difference between Hy1 and AH I° was calculated to be approx. 15 kJ mol-1. The second anhydrate polymorph (AH II) can be obatined from the quench cooled melt of o-phen, but is unstable at ambient conditions and transforms wihtin minutes to either AH I° or Hy1. The two neat polymorphs are enantiotropically related and water-free o-phen transforms to Hy1 at RH > 16%. The structural and stablity features of the solid forms, in paricular Hy1, are unravelled by a combination of experimental (thermal analysis, moisture sorption/desorption and storage experiments, infrared spectroscopy and powder X-ray diffraction) and computational modelling (crystal structure prediction and lattice energy calculations), providing a consistent picture why o-phen forms a very stable Z' = 3 channel hydrate.

Probability distribution of surface wind speed induced by convective adjustment on Venus

The influence of convective adjustment on the spatial structure of Venusian surface wind and probability distribution of its wind speed is investigated using an idealized weather research and forecasting model. When the initially uniform wind is much weaker than the convective wind, patches of both prograde and retrograde winds with scales of a few kilometers are formed during active convective adjustment. After the active convective adjustment, because the small-scale convective cells and their related vertical momentum fluxes dissipate quickly, the large-scale (>4km) prograde and retrograde wind patches remain on the surface and in the longitude–height cross-section. This suggests the coexistence of local prograde and retrograde flows, which may correspond to those observed by Pioneer Venus below 10km altitude. The probability distributions of surface wind speed V during the convective adjustment have a similar form in different simulations, with a sharp peak around ∼0.1ms–1 and a bulge developing on the flank of the probability distribution. This flank bulge is associated with the most active convection, which has a probability distribution with a peak at the wind speed 1.5-times greater than the Weibull fitting parameter c during the convective adjustment. The Weibull distribution P(>V) (= exp[−(V/c)k]) with best-estimate coefficients of Lorenz (2016) is reproduced during convective adjustments induced by a potential energy of ∼7 ×107Jm−2, which is calculated from the difference in total potential energy between initially unstable and neutral states. The maximum vertical convective heat flux magnitude is proportional to the potential energy of the convective adjustment in the experiments with the initial unstable-layer thickness altered. The present work suggests that convective adjustment is a promising process for producing the wind structure with occasionally generating surface winds of ∼1ms–1 and retrograde wind patches.

Thermodynamics of adaptive molecular resolution.

A relatively general thermodynamic formalism for adaptive molecular resolution (AMR) is presented. The description is based on the approximation of local thermodynamic equilibrium and considers the alchemic parameter λ as the conjugate variable of the potential energy difference between the atomistic and coarse-grained model Φ=U(1)-U(0) The thermodynamic formalism recovers the relations obtained from statistical mechanics of H-AdResS (Español et al, J. Chem. Phys. 142, 064115, 2015 (doi:10.1063/1.4907006)) and provides relations between the free energy compensation and thermodynamic potentials. Inspired by this thermodynamic analogy, several generalizations of AMR are proposed, such as the exploration of new Maxwell relations and how to treat λ and Φ as 'real' thermodynamic variablesThis article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Nonhysteretic superelasticity and strain hardening in a copper bicrystal with a ∑3{112} twin boundary

Superelasticity in nanoscale materials is of profound fundamental interest. Despite extensive research into low-dimensional systems such as nanowires and nanobeams, no compelling evidence exists for superelasticity in high-dimensional systems. Here, we demonstrate that a copper bicrystal with a ∑3{112} twin boundary (TB) during shear loading and unloading cycles exhibits nonhysteretic superelasticity. The upper bound of total recoverable shear strain associated with superelastic deformation is 24.8%. ∑3{112} TB under shear loading dissociates into two phase boundaries (PBs) with different characteristics, constituted by two phases with FCC and 9R structures. The transformation between these two phases, assisted by the reversible migration of tilt PB during loading and unloading cycles, accounts for the superelasticity. The driving force for the superelasticity is the potential energy difference per atom of the two phases. However, the irreversible migration of mixed tilt/twist PB with energy dissipation is responsible for strain hardening. This work, the first observation of nonhysteretic superelasticity in a copper bicrystal, may shed light on the design of bulk materials with superelasticity.

Artificial upwelling using offshore wind energy for mariculture applications

Offshore wind is proposed as an energy source to upwell nutrient-rich deep water to the ocean photic layers. A spar-buoy wind turbine with a rigid tube about 300 m long is proposed as a pipe to drive deep water up to the surface. The minimum energy required to uplift the water is the potential energy difference between surface waters inside and outside the pipe, which depends on the background density profile. The corresponding surface jump or hydraulic head, h, calculated for several analytical and experimental density profiles, is of the order of 10 cm. If the complete turbine power (of the order of several MW) is used for raising the water (assuming a 100% pump efficiency), in a frictionless flow, very large water volumes, of the order of thousands of m 3 s -1 , will be transported to the photic layers. In a more realistic case, taking into account pipe friction in wide pipes, of the order of 10 m radius, and a power delivered to the fluid of 1 MW, the volume transport is still very large, about 500 m 3 s -1 . However, such a large amount of dense water could sink fast to aphotic layers due to vertical static instability ( the fountain effect ), ruining the enhancement of primary production. Hence, some ways to increase the turbulent entrainment and avoid the fountain effect are proposed. From the energetic viewpoint, artificial upwelling using offshore wind energy is a promising way to fertilize large open sea regions. This mariculture application is, however, severely subjected to atmosphere and ocean climatology, as well as to ecological dynamics. The general problem is multidisciplinary, and some important physical, engineering and ecological questions need to be seriously addressed to improve our confidence in the approach presented here.

Improved Sugar Puckering Profiles for Nicotinamide Ribonucleoside for Hybrid QM/MM Simulations.

The coenzyme nicotinamide adenine dinucleotide (NAD+) and its reduced form (NADH) play ubiquitous roles as oxidizing and reducing agents in nature. The binding, and possibly the chemical redox step, of NAD+/NADH may be influenced by the cofactor conformational distribution and, in particular, by the ribose puckering of its nicotinamide-ribonucleoside (NR) moiety. In many hybrid quantum mechanics-molecular mechanics (QM/MM) studies of NAD+/NADH dependent enzymes, the QM region is treated by semiempirical (SE) methods. Recent work suggests that SE methods do not adequately describe the ring puckering in sugar molecules. In the present work we adopt an efficient and practical strategy to correct for this deficiency for NAD+/NADH. We have implemented a cost-effective correction to a SE Hamiltonian by adding a correction potential, which is defined as the difference between an accurate benchmark density functional theory (DFT) potential energy surface (PES) and the SE PES. In practice, this is implemented via a B-spline interpolation scheme for the grid-based potential energy difference surface. We find that the puckering population distributions obtained from free energy QM(SE)/MM simulations are in good agreement with DFT and in fair accord with experimental results. The corrected PES should facilitate a more accurate description of the ribose puckering in the NAD+/NADH cofactor in simulations of biological systems.

Study of Flexoelectricity in Graphene Composite Structures

ABSTRACTThis paper introduces the theoretical and experimental investigation of flexoelectric behavior in a graphene composite structure consisting of multilayer CVD-graphene deposited on an ALD-platinum catalyst layer deposited on top of n-silicon substrate. The polarization induced by varying the radius of curvature from 200–1500 mm by applying bending stresses was investigated experimentally. Meanwhile, due to the cluster-growth nature of the ALD-platinum catalyst layer, a strong correlation was observed between the resulting number of graphene layers and the Pt catalyst layer thickness, which subsequently had a strong impact on the induced polarization. A polarization current of up to 7.4 mA was detected when the composite structure was bent through a 600-mm radius of curvature. Residual stresses at the interface of the different layers were estimated experimentally in the order of 85–217 MPa. The effect of thermally-induced stresses, residual stresses at the interface layers, thickness of graphene layers, and radius of curvature were investigated theoretically using the finite element method (FEM) and first-principle analyses. Theoretically, it was confirmed that non-uniform strain results in an appreciable non-uniform graphene band gap opening, in addition to non-uniform change of the band structure across the surface and thickness which results in increasing the potential energy difference between the graphene layers. FEM confirmed that thermally induced strains could further enhance the power output of the device by inducing a flexoelectric current combined with the thermionic response. This is verified by estimating a lattice displacement up to 0.31 Å in response to 2-mW heat flux, which corresponds to an appreciable graphene band opening and a potential energy difference across the graphene layers in the order of 1.23 eV, as estimated by the tight binding model.

Visualizing Vapor Pressure: A Mechanical Demonstration of Liquid–Vapor Phase Equilibrium

Abstract Water phase transitions are central to climate and weather. Yet it is a common experience that the principles of phase equilibrium are challenging to understand and teach. A simple mechanical analogy has been developed to demonstrate key principles of liquid evaporation and the temperature dependence of equilibrium vapor pressure. The system is composed of a circular plate with a central depression and several hundred metal balls. Mechanical agitation of the plate causes the balls to bounce and interact in much the same statistical way that molecules do in real liquid–vapor systems. The data, consisting of the number of balls escaping the central well at different forcing energies, exhibit a logarithmic dependence on the reciprocal of the applied energy (analogous to thermal energy kBT) that is similar to that given by Boltzmann statistics and the Clausius–Clapeyron equation. These results demonstrate that the enthalpy (i.e., latent heat) of evaporation is well interpreted as the potential energy difference between molecules in the vapor and liquid phases, and it is the fundamental driver of vapor pressure increase with temperature. Consideration of the uncertainties in the measurements shows that the mechanical system is described well by Poisson statistics. The system is simple enough that it can be duplicated for qualitative use in atmospheric science teaching, and an interactive animation based on the mechanical system is available online for instructional use (http://phy.mtu.edu/vpt/).

The potential energy landscape for crystallisation of a Lennard-Jones fluid

Crystallisation pathways are explored by direct analysis of the potential energy landscape for a system of Lennard-Jones particles with periodic boundary conditions. A database of minima and transition states linking liquid and crystalline states is constructed using discrete path sampling and the entire potential energy landscape from liquid to crystal is visualised. We demonstrate that there is a strong negative correlation between the number of atoms in the largest crystalline cluster and the potential energy. In common with previous results we find a strong bias towards the growth of FCC rather than HCP clusters, despite a very small potential energy difference. We characterise three types of perfect crystals with very similar energies: pure FCC, pure HCP, and combinations of FCC and HCP layers. There are also many slightly defective crystalline structures. The effect of the simulation box is analysed for a supercell containing 864 atoms. There are low barriers between some of the different crystalline structures via pathways involving sliding layers, and many different defective structures with FCC layers stacked at an angle to the periodic box. Finally, we compare a binary Lennard-Jones system and visualise the potential energy landscape from supercooled liquid to crystal.

Effect of fiber clustering on debond growth energy release rate in UD composites with hexagonal packing

Steady-state energy release rate (ERR) for fiber/matrix interface debond growth originated from fiber break in unidirectional composite is calculated using 3-D FEM models with hexagonal fiber arrangement. In the model the debonded fiber is central in the hexagonal unit which is surrounded by effective composite. The effect of neighboring fibers focusing on local fiber clustering on the ERR is analyzed by varying the distance between fibers in the unit. The steady-state ERR is calculated from potential energy difference between a unit in the bonded region far ahead of the debond front and a unit in the debonded region far behind the debond front. The ERR for different modes of crack propagation is obtained from a FEM model containing a long debond by analyzing the stress at the debond front.Results show that in mechanical axial tensile loading fracture Mode II is dominating, it has strong angular dependence (effect of closest fibers) but the average ERR is not sensitive to the local fiber clustering. In thermal loading the Mode III is dominating and the average ERR is highly dependent on the distance to neighboring fibers. However, for realistic loads the thermal ERR is much smaller than the mechanical.

Effect of structural defects towards the performance of TiO2/SnO2/WO3 photocatalyst in the degradation of 1,2-dichlorobenzene

In this study, the effect of surface/structural defects of TiO2/SnO2/WO3 trimetallic oxide on the photocatalytic activity was investigated. Two sets of trimetallic oxide were prepared by mechanical mixing of the pure TiO2, WO3 and SnO2 with exposed facets synthesized by sol–gel and hydrothermal methods. These photocatalysts were characterized by XRD, DRUV, PL, FESEM, TEM and XPS. Comparison of the photocatalytic degradation of 1,2-dichlorobenzene was done under UV and visible light. The results showed that the trimetallic oxide prepared from hydrothermal exhibited higher photocatalytic activity under visible light compared to the sol–gel prepared photocatalyst. Based on the characterization, it could be deduced that the high photocatalytic activity was attributed to the synergistic effect of several factors such as the exposed facets, presence of Ti3+ and charge transfer (revealed by XPS) between the metal oxides through the heterojunction (from TEM image) formation. The charge transfer was further projected through a schematic diagram that showed the potential energy differences at the valence band and conduction band of the metal oxides.

Asymmetry in the triplet 3p-4s Mg lines in cool DZ white dwarfs

The purpose of the present work is to make an exhaustive study of the line shape of the triplet 3p-4s Mg line (Mgb triplet), which is perturbed by He in the extreme physical conditions found in the cool atmosphere of DZ white dwarfs. This study is undertaken by inferring both a unified theory of spectral line broadening and ab initio potential energies. Cool white dwarfs require a specific treatment for line broadening owing to the high helium densities that are involved. Beyond the conventional symmetrical Lorentzian core at low density, we show that the line profiles are asymmetrical and have significant additional contributions on the short wavelength side. This blue asymmetry is a consequence of low maxima in the corresponding Mg-He potential energy difference curves at short and intermediate internuclear distances. The new profiles are shown to provide a good fit to an SDSS (Sloan Digital Sky Survey) observation.