Orkan Umurhan | NASA-Ames Research Center (original) (raw)
Papers by Orkan Umurhan
Icarus, 2018
We conclude that Bladed Terrain on Pluto is a deposit of massive CH4, which preferentially precip... more We conclude that Bladed Terrain on Pluto is a deposit of massive CH4, which preferentially precipitates at high elevations, and has since its initial formation, undergone episodes of sublimation erosion that has given this deposit its characteristic texture.
Context. Simulations of astrophysical disks in the shearing box that are subject to the magnetoro... more Context. Simulations of astrophysical disks in the shearing box that are subject to the magnetorotational instability (MRI) show that activity appears to be reduced as the magnetic Prandtl number Pm is lowered. It is therefore important to understand the reasons for this trend, especially if this trend is shown to continue when higher resolution calculations are performed in the near future. Calculations for laboratory experiments show that saturation is achieved through modification of the background shear for Pm ≪ 1. Aims. Guided by the results of calculations appropriate for laboratory experiments when Pm is very low, the stability of inviscid disturbances in a shearing box model immersed in a constant vertical background magnetic field is considered under a variety of shear profiles and boundary conditions in order to evaluate the hypothesis that modifications of the shear bring about saturation of the instability. Shear profiles q are given by the local background Keplerian mean, q0, plus time-independent departures, Q(x), with zero average on a given scale. Methods. The axisymmetric linear stability of inviscid magnetohydrodynamic normal modes in the shearing box is analyzed. Results. (i) The stability/instability of modes subject to modified shear profiles may be interpreted by a generalized Velikhov criterion given by an effective shear and radial wavenumber that are defined by the radial structure of the mode and the form of Q. (ii) Where channel modes occur, comparisons against marginally unstable disturbance in the classical case, Q = 0, shows that all modifications of the shear examined here enhance mode instability. (iii) For models with boundary conditions mimicing laboratory experiments, modified shear profiles exist that stabilize a marginally unstable MRI for Q = 0. (iv) Localized normal modes on domains of infinite radial extent characterized by either single defects or symmetric top-hat profiles for Q are also investigated. If the regions of modified shear are less (greater) than the local Keplerian background, then there are (are no) normal modes leading to the MRI. Conclusions. The emergence and stability of the MRI is sensitive to the boundary conditions adopted. Channel modes do not appear to be stabilized through modifications of the background shear whose average remains Keplerian. However, systems that have non-penetrative boundaries can saturate the MRI through modification of the background shear. Conceptually equating the qualitative results from laboratory experiments to the conditions in a disk may therefore be misleading.
This brief summarizes work devoted to studying the linear stability of baroclinic pro-toplanetary... more This brief summarizes work devoted to studying the linear stability of baroclinic pro-toplanetary Keplerian disks. This work largely builds on the foundation and fundamental results obtained by Barranco, Marcus & Umurhan (2000) (hereafter BMU) which pre-sented a model to describe structures in weakly baroclinic Keplerian disks. Interest in protoplanetary disks has grown since the discovery of the rst of what are now dozens of extrasolar planets around F and G type stars (Marcy 1996, Perryman 2000). The apparent ubiquity of planets suggests that the nebular disks (or protoplan-etary disks), out of which these stars are born, must be susceptible to the development of structures. However, theoretical work (see references in BMU) argues that purely pressure-supported gaseous barotropic Keplerian disks do not undergo any known type of hydrodynamic instabilities. The basis for this claim is that the strong rotation in Keplerian shear flows manages to suppress any of the usual instabilities seen in labora-tory shear flows such as the Taylor-Couette and Kelvin-Helmholtz instabilities (Drazin & Reid, 1982). Some investigators (e.g. Shu et al., 1993) have gone so far as to claim that protoplanetary disks are featureless objects totally bereft of vortical structures or
Monthly Notices of the Royal Astronomical Society, 2016
Journal of Geophysical Research: Planets, 2015
Callisto's pinnacle terrain has been interpreted to form through sublimation weathering of bedroc... more Callisto's pinnacle terrain has been interpreted to form through sublimation weathering of bedrock and subsequent deposition of the sublimated ice in local cold traps on peaks and crater rims. To investigate how these processes are affected by environmental parameters, including solar illumination and the composition and concentration of ices in the crust, we employ the MARSSIM landform evolution model and advance its treatment of the physics that underlies the relevant processes. Both ice sublimation and deposition are controlled by surface temperature, which we calculate based on energy contributions from both insolation and thermal reradiation from the surrounding landscape. We perform 4.5 Gyr duration simulations whereby we separately consider and model CO 2 and H 2 O as the crustal ice species. We find that sublimating a crustal content of 10% CO 2 ice (a reasonable but arbitrarily selected value) yields present-day landform degradation and regolith coverage that is comparable to what is observed on Callisto. In our H 2 O ice simulations we reproduce the essential features of pinnacle ice distribution at both the equator and midlatitudes. Our present nominal crustal H 2 O ice content is 33%, which produces a maximum pinnacle ice thickness of 64 m. Pinnacle height is likely limited by collapse or mass wasting of the ice once it reaches a certain thickness. WHITE ET AL.
We examine the stability of nonadiabatic acoustic modes in a plane parallel atmosphere in a const... more We examine the stability of nonadiabatic acoustic modes in a plane parallel atmosphere in a constant gravitational field where the source of nonadiabaticity is thermal conduction with constant coefficient. This prescription filters out the effects of the kappa -mechanism. The static state is described by polytrope solutions where the density is related to the linear temperature profile via a power
ABSTRACT A physical mechanism for enhanced angular momentum transport (AMT) outwards is needed fo... more ABSTRACT A physical mechanism for enhanced angular momentum transport (AMT) outwards is needed for the theoretical modeling of accretion disks (ADs) in e.g. Cataclysmic Variables (CVs). It is clear that ordinary microscopic viscosity is out of the question - the time scale of transport it dictates is many orders of magnitude longer than the one deduced from mass accretion rate consistent with observations. It is however reasonable that turbulent transport can provide the needed timescale value. Astrophysicists have persistently looked for an linear instability in ADs, which can ultimately lead to turbulence. In this contribution we dispute the "common knowledge", accepted during the last two decades or so, that the magneto-rotational instability (MRI) is the physical agent that destabilizes thin ADs and ultimately drives turbulence and AMT. We also suggest, thus, that we do not yet have at our disposal any better model for AMT than the30 year old alpha model
So-called "ASTRO 101'' survey courses in general astronomy are offered to non-scie... more So-called "ASTRO 101'' survey courses in general astronomy are offered to non-science majors in colleges and universities across the United States, to fulfill general-education requirements in the physical sciences. At least two of the common Student Learning Outcomes (SLO) for these courses are critical thinking and understanding astronomy as a scientific discipline. We argue that a comprehensive lower-division astronomy program surpassing ASTRO 101 would increase science literacy for non-science majors, STEM students, and the general public. The program would include diverse astronomy course offerings, interdisciplinary science courses (e.g. astrobiology), service-learning and peer-mentoring activities, and internship opportunities.
Solid State Ionics, 2008
ABSTRACT The I–V relations found for the system metal|semiconductor|metal with chemically inert e... more ABSTRACT The I–V relations found for the system metal|semiconductor|metal with chemically inert electrodes are not always as one would expect from the common theory of semiconductivity. The problem can be traced back to motion of ionic defects, i.e. the acceptors (or donors) in the semiconductor. We here discuss the parameters, equations and physical constraints that have to be taken into consideration when evaluating the I–V relations of that system in the presence of motion of the ionic defects. For comparison another model, that of electron hopping in the band of dopant impurity states, is also discussed. I–V relations and the defect distributions depend on three main factors: the contact potentials at the semiconductor/metal-electrode, the thickness of the sample and the degree of ionization of the dopant. A variety of I–V relations are obtained for different values of the controlling parameters. This explains the diversity in the I–V relations reported for systems of the form metal|semiconductor|metal.
Solid State Ionics, 2008
ABSTRACT A device of the form Metal1|MIEC|Metal2 is discussed, MIEC being a mixed ionic electroni... more ABSTRACT A device of the form Metal1|MIEC|Metal2 is discussed, MIEC being a mixed ionic electronic conductor which is assumed to include one mobile ionic defect (acceptors) and one electronic defect (holes). The two electrodes are assumed to be inert and blocking for material exchange. The defect distribution and I–V relations are solved numerically assuming steady-state and local equilibrium. The effects of acceptor ionization, contact potentials and space charge are taken into consideration. Different thicknesses, from nano to macro, are considered as well as different contact potentials. The results are compared with the local neutrality (analytic) limit. It is found that the device when based on thin MIEC and certain a-symmetric contact potentials shows rectification somewhat similar to a classic Schottky diode, implying that aging process may not be a real problem.A second model is considered in which the ionic motion is replaced by electron hopping between acceptors. The model is solved numerically for the defect distributions and I–V relations. This and the previous models are compared for different thicknesses and contact potentials. The two models may present one of four families of I–V curves (though each model may exhibit them under different conditions). Thus the hopping process cannot be distinguished from the one with ionic motion by just examining the I–V relations and further information is required for identifying the model.
Solid State Ionics, 2007
ABSTRACT The characteristics of solid state devices based on p-type semiconductors with mobile ac... more ABSTRACT The characteristics of solid state devices based on p-type semiconductors with mobile acceptors are discussed. The devices are basic ones of the form: metal|semiconductor|metal. The metal electrodes are assumed to be chemically inert and to block material exchange. The effect of the contact potentials as well as of the space charge are taken into consideration. The distribution of charge carriers (holes and acceptors) and the I–V relations are evaluated. These results are compared with those of a model in which the acceptors are immobile and with two approximations in which neutrality is assumed either at the boundary or throughout the whole semiconductor. The motion of the acceptors is found, in some cases, to introduce only minor changes in the I–V relations. This finding may be of significance for solid state devices of reduced scale. The I–V relations of samples much thicker than the equilibrium Debye length reduce to the ones obtained assuming local neutrality throughout the sample. The results also depend significantly on the reaction constant between the acceptors and holes to form neutral acceptors.
Physical Review E, 2007
We study the saturation near threshold of the axisymmetric magnetorotational instability ͑MRI͒ of... more We study the saturation near threshold of the axisymmetric magnetorotational instability ͑MRI͒ of a viscous, resistive, incompressible fluid in a thin-gap Taylor-Couette configuration. A vertical magnetic field, Keplerian shear, and no-slip conducting radial boundary conditions are adopted. The weakly nonlinear theory leads to a real Ginzburg-Landau equation for the disturbance amplitude, as in our previous idealized analysis. For small magnetic Prandtl number ͑P m 1͒, the saturation amplitude scales as P m 2/3 while the magnitude of angular momentum transport scales as P m 4/3. The difference from the previous scalings ͑proportional to P m 1/2 and P m respectively͒ is attributed to the emergence of radial boundary layers. Away from those, steady-state nonlinear saturation is achieved through a modest reduction in the destabilizing shear. These results will be useful in understanding MRI laboratory experiments and associated numerical simulations.
Monthly Notices of the Royal Astronomical Society, 2013
We analyse the stability and nonlinear dynamical evolution of power-law accretion disc models. Th... more We analyse the stability and nonlinear dynamical evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are strict power-law functions of cylindrical radius, R. We employ two different hydrodynamic codes to perform high resolution 2D-axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the thermal relaxation time of the fluid, and the disc viscosity. We present an accompanying stability analysis of the problem, based on asymptotic methods, that we use to interpret the results of the simulations. We find that axisymmetric disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of modes with wavenumber ratios |k R /k Z | 1 when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time scale. These discs are subject to the Goldreich-Schubert-Fricke (GSF) or 'vertical shear' linear instability. Development of the instability involves excitation of vertical breathing and corrugation modes in the disc, with the corrugation modes in particular being a feature of the nonlinear saturated state. Instability is found to operate when the dimensionless disc kinematic viscosity ν < 10 −6 , corresponding to Reynolds numbers Re = Hc s /ν > 2500. In three dimensions the instability generates a quasiturbulent flow, and the associated Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches α ∼ 6 × 10 −4 by the end of the simulation. The evolution and saturation of the vertical shear instability in astrophysical disc models which include realistic treatments of the thermal physics has yet to be examined. Should it occur on either global or local scales, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties, and observational appearance.
Monthly Notices of the Royal Astronomical Society, 2006
The linear normal-mode stratorotational instability (SRI) is analytically reexamined in the invis... more The linear normal-mode stratorotational instability (SRI) is analytically reexamined in the inviscid limit where the length scales of horizontal disturbances are large compared their vertical and radial counterparts. Boundary conditions different than channel walls are also considered. This quasi-hydrostatic, semi-geostrophic (QHSG) approximation allows one to examine the effect of a vertically varying Brunt-Vaisaila frequency, N 2. It is found that the normal-mode instability persists when N 2 increases quadratically with respect to the disc vertical coordinate. However we also find that the SRI seems to exist in this inviscid QHSG extreme only for channel wall conditions: when one or both of the reflecting walls are removed there is no instability in the asymptotic limit explored here. It is also found that only exponential-type SRI modes (as defined by Dubrulle et al. 2005) exist under these conditions. These equations also admit non-normal mode behaviour. Fixed Lagrangian pressure conditions on both radial boundaries predicts there to be no normal mode behaviour in the QHSG limit. The mathematical relationship between the results obtained here and that of the classic Eady (1949) problem for baroclinic instability is drawn. We conjecture as to the mathematical/physical nature of the SRI. The general linear problem, analyzed without approximation in the context of the Boussinesq equations, admits a potential vorticity-like quantity that is advectively conserved by the shear. Its existence means that a continuous spectrum is a generic feature of this system. It also implies that in places where the Brunt-Vaisaila frequency becomes dominant the linearized flow may two-dimensionalize by advectively conserving its vertical vorticity.
Journal of the Atmospheric Sciences, 2008
Motivated by the success of potential vorticity (PV) thinking for Rossby waves and related shear ... more Motivated by the success of potential vorticity (PV) thinking for Rossby waves and related shear flow phenomena, this work develops a buoyancy–vorticity formulation of gravity waves in stratified shear flow, for which the nonlocality enters in the same way as it does for barotropic/baroclinic shear flows. This formulation provides a time integration scheme that is analogous to the time integration of the quasigeostrophic equations with two, rather than one, prognostic equations, and a diagnostic equation for streamfunction through a vorticity inversion. The invertibility of vorticity allows the development of a gravity wave kernel view, which provides a mechanistic rationalization of many aspects of the linear dynamics of stratified shear flow. The resulting kernel formulation is similar to the Rossby-based one obtained for barotropic and baroclinic instability; however, since there are two independent variables—vorticity and buoyancy—there are also two independent kernels at each l...
Journal of Applied Physics, 2008
ABSTRACT Current-voltage relations, electric field, and charge distribution profiles are calculat... more ABSTRACT Current-voltage relations, electric field, and charge distribution profiles are calculated for a device in which the dopants are mobile. The thin film limit is discussed. The model solved is restricted to: (a) mobile holes and acceptors, (b) steady state, and (c) metal electrodes which block the ionic current. The solution is expressed as a series expansion in the small parameter delta=L/lambdaD, where L is the sample thickness and lambdaD is a Debye length. The second order of the series expansion is found to vanish, thus the corrections to the leading order appear only in the third term. The approximated analytic solution agrees with numerical results from a previous publication up to the quite high value of delta=1. The leading order in the I-V relations and in the hole distribution is independent of the acceptor motion. This implies that for thin devices of this form any motion of the dopants may be neglected and that dopants need not be limited only to those which exhibit low diffusion constants. Rectification is observed as long as asymmetry is introduced by two different contact potentials. This holds whether the contacts lead to depletion or accumulation.
Icarus, 2018
We conclude that Bladed Terrain on Pluto is a deposit of massive CH4, which preferentially precip... more We conclude that Bladed Terrain on Pluto is a deposit of massive CH4, which preferentially precipitates at high elevations, and has since its initial formation, undergone episodes of sublimation erosion that has given this deposit its characteristic texture.
Context. Simulations of astrophysical disks in the shearing box that are subject to the magnetoro... more Context. Simulations of astrophysical disks in the shearing box that are subject to the magnetorotational instability (MRI) show that activity appears to be reduced as the magnetic Prandtl number Pm is lowered. It is therefore important to understand the reasons for this trend, especially if this trend is shown to continue when higher resolution calculations are performed in the near future. Calculations for laboratory experiments show that saturation is achieved through modification of the background shear for Pm ≪ 1. Aims. Guided by the results of calculations appropriate for laboratory experiments when Pm is very low, the stability of inviscid disturbances in a shearing box model immersed in a constant vertical background magnetic field is considered under a variety of shear profiles and boundary conditions in order to evaluate the hypothesis that modifications of the shear bring about saturation of the instability. Shear profiles q are given by the local background Keplerian mean, q0, plus time-independent departures, Q(x), with zero average on a given scale. Methods. The axisymmetric linear stability of inviscid magnetohydrodynamic normal modes in the shearing box is analyzed. Results. (i) The stability/instability of modes subject to modified shear profiles may be interpreted by a generalized Velikhov criterion given by an effective shear and radial wavenumber that are defined by the radial structure of the mode and the form of Q. (ii) Where channel modes occur, comparisons against marginally unstable disturbance in the classical case, Q = 0, shows that all modifications of the shear examined here enhance mode instability. (iii) For models with boundary conditions mimicing laboratory experiments, modified shear profiles exist that stabilize a marginally unstable MRI for Q = 0. (iv) Localized normal modes on domains of infinite radial extent characterized by either single defects or symmetric top-hat profiles for Q are also investigated. If the regions of modified shear are less (greater) than the local Keplerian background, then there are (are no) normal modes leading to the MRI. Conclusions. The emergence and stability of the MRI is sensitive to the boundary conditions adopted. Channel modes do not appear to be stabilized through modifications of the background shear whose average remains Keplerian. However, systems that have non-penetrative boundaries can saturate the MRI through modification of the background shear. Conceptually equating the qualitative results from laboratory experiments to the conditions in a disk may therefore be misleading.
This brief summarizes work devoted to studying the linear stability of baroclinic pro-toplanetary... more This brief summarizes work devoted to studying the linear stability of baroclinic pro-toplanetary Keplerian disks. This work largely builds on the foundation and fundamental results obtained by Barranco, Marcus & Umurhan (2000) (hereafter BMU) which pre-sented a model to describe structures in weakly baroclinic Keplerian disks. Interest in protoplanetary disks has grown since the discovery of the rst of what are now dozens of extrasolar planets around F and G type stars (Marcy 1996, Perryman 2000). The apparent ubiquity of planets suggests that the nebular disks (or protoplan-etary disks), out of which these stars are born, must be susceptible to the development of structures. However, theoretical work (see references in BMU) argues that purely pressure-supported gaseous barotropic Keplerian disks do not undergo any known type of hydrodynamic instabilities. The basis for this claim is that the strong rotation in Keplerian shear flows manages to suppress any of the usual instabilities seen in labora-tory shear flows such as the Taylor-Couette and Kelvin-Helmholtz instabilities (Drazin & Reid, 1982). Some investigators (e.g. Shu et al., 1993) have gone so far as to claim that protoplanetary disks are featureless objects totally bereft of vortical structures or
Monthly Notices of the Royal Astronomical Society, 2016
Journal of Geophysical Research: Planets, 2015
Callisto's pinnacle terrain has been interpreted to form through sublimation weathering of bedroc... more Callisto's pinnacle terrain has been interpreted to form through sublimation weathering of bedrock and subsequent deposition of the sublimated ice in local cold traps on peaks and crater rims. To investigate how these processes are affected by environmental parameters, including solar illumination and the composition and concentration of ices in the crust, we employ the MARSSIM landform evolution model and advance its treatment of the physics that underlies the relevant processes. Both ice sublimation and deposition are controlled by surface temperature, which we calculate based on energy contributions from both insolation and thermal reradiation from the surrounding landscape. We perform 4.5 Gyr duration simulations whereby we separately consider and model CO 2 and H 2 O as the crustal ice species. We find that sublimating a crustal content of 10% CO 2 ice (a reasonable but arbitrarily selected value) yields present-day landform degradation and regolith coverage that is comparable to what is observed on Callisto. In our H 2 O ice simulations we reproduce the essential features of pinnacle ice distribution at both the equator and midlatitudes. Our present nominal crustal H 2 O ice content is 33%, which produces a maximum pinnacle ice thickness of 64 m. Pinnacle height is likely limited by collapse or mass wasting of the ice once it reaches a certain thickness. WHITE ET AL.
We examine the stability of nonadiabatic acoustic modes in a plane parallel atmosphere in a const... more We examine the stability of nonadiabatic acoustic modes in a plane parallel atmosphere in a constant gravitational field where the source of nonadiabaticity is thermal conduction with constant coefficient. This prescription filters out the effects of the kappa -mechanism. The static state is described by polytrope solutions where the density is related to the linear temperature profile via a power
ABSTRACT A physical mechanism for enhanced angular momentum transport (AMT) outwards is needed fo... more ABSTRACT A physical mechanism for enhanced angular momentum transport (AMT) outwards is needed for the theoretical modeling of accretion disks (ADs) in e.g. Cataclysmic Variables (CVs). It is clear that ordinary microscopic viscosity is out of the question - the time scale of transport it dictates is many orders of magnitude longer than the one deduced from mass accretion rate consistent with observations. It is however reasonable that turbulent transport can provide the needed timescale value. Astrophysicists have persistently looked for an linear instability in ADs, which can ultimately lead to turbulence. In this contribution we dispute the "common knowledge", accepted during the last two decades or so, that the magneto-rotational instability (MRI) is the physical agent that destabilizes thin ADs and ultimately drives turbulence and AMT. We also suggest, thus, that we do not yet have at our disposal any better model for AMT than the30 year old alpha model
So-called "ASTRO 101'' survey courses in general astronomy are offered to non-scie... more So-called "ASTRO 101'' survey courses in general astronomy are offered to non-science majors in colleges and universities across the United States, to fulfill general-education requirements in the physical sciences. At least two of the common Student Learning Outcomes (SLO) for these courses are critical thinking and understanding astronomy as a scientific discipline. We argue that a comprehensive lower-division astronomy program surpassing ASTRO 101 would increase science literacy for non-science majors, STEM students, and the general public. The program would include diverse astronomy course offerings, interdisciplinary science courses (e.g. astrobiology), service-learning and peer-mentoring activities, and internship opportunities.
Solid State Ionics, 2008
ABSTRACT The I–V relations found for the system metal|semiconductor|metal with chemically inert e... more ABSTRACT The I–V relations found for the system metal|semiconductor|metal with chemically inert electrodes are not always as one would expect from the common theory of semiconductivity. The problem can be traced back to motion of ionic defects, i.e. the acceptors (or donors) in the semiconductor. We here discuss the parameters, equations and physical constraints that have to be taken into consideration when evaluating the I–V relations of that system in the presence of motion of the ionic defects. For comparison another model, that of electron hopping in the band of dopant impurity states, is also discussed. I–V relations and the defect distributions depend on three main factors: the contact potentials at the semiconductor/metal-electrode, the thickness of the sample and the degree of ionization of the dopant. A variety of I–V relations are obtained for different values of the controlling parameters. This explains the diversity in the I–V relations reported for systems of the form metal|semiconductor|metal.
Solid State Ionics, 2008
ABSTRACT A device of the form Metal1|MIEC|Metal2 is discussed, MIEC being a mixed ionic electroni... more ABSTRACT A device of the form Metal1|MIEC|Metal2 is discussed, MIEC being a mixed ionic electronic conductor which is assumed to include one mobile ionic defect (acceptors) and one electronic defect (holes). The two electrodes are assumed to be inert and blocking for material exchange. The defect distribution and I–V relations are solved numerically assuming steady-state and local equilibrium. The effects of acceptor ionization, contact potentials and space charge are taken into consideration. Different thicknesses, from nano to macro, are considered as well as different contact potentials. The results are compared with the local neutrality (analytic) limit. It is found that the device when based on thin MIEC and certain a-symmetric contact potentials shows rectification somewhat similar to a classic Schottky diode, implying that aging process may not be a real problem.A second model is considered in which the ionic motion is replaced by electron hopping between acceptors. The model is solved numerically for the defect distributions and I–V relations. This and the previous models are compared for different thicknesses and contact potentials. The two models may present one of four families of I–V curves (though each model may exhibit them under different conditions). Thus the hopping process cannot be distinguished from the one with ionic motion by just examining the I–V relations and further information is required for identifying the model.
Solid State Ionics, 2007
ABSTRACT The characteristics of solid state devices based on p-type semiconductors with mobile ac... more ABSTRACT The characteristics of solid state devices based on p-type semiconductors with mobile acceptors are discussed. The devices are basic ones of the form: metal|semiconductor|metal. The metal electrodes are assumed to be chemically inert and to block material exchange. The effect of the contact potentials as well as of the space charge are taken into consideration. The distribution of charge carriers (holes and acceptors) and the I–V relations are evaluated. These results are compared with those of a model in which the acceptors are immobile and with two approximations in which neutrality is assumed either at the boundary or throughout the whole semiconductor. The motion of the acceptors is found, in some cases, to introduce only minor changes in the I–V relations. This finding may be of significance for solid state devices of reduced scale. The I–V relations of samples much thicker than the equilibrium Debye length reduce to the ones obtained assuming local neutrality throughout the sample. The results also depend significantly on the reaction constant between the acceptors and holes to form neutral acceptors.
Physical Review E, 2007
We study the saturation near threshold of the axisymmetric magnetorotational instability ͑MRI͒ of... more We study the saturation near threshold of the axisymmetric magnetorotational instability ͑MRI͒ of a viscous, resistive, incompressible fluid in a thin-gap Taylor-Couette configuration. A vertical magnetic field, Keplerian shear, and no-slip conducting radial boundary conditions are adopted. The weakly nonlinear theory leads to a real Ginzburg-Landau equation for the disturbance amplitude, as in our previous idealized analysis. For small magnetic Prandtl number ͑P m 1͒, the saturation amplitude scales as P m 2/3 while the magnitude of angular momentum transport scales as P m 4/3. The difference from the previous scalings ͑proportional to P m 1/2 and P m respectively͒ is attributed to the emergence of radial boundary layers. Away from those, steady-state nonlinear saturation is achieved through a modest reduction in the destabilizing shear. These results will be useful in understanding MRI laboratory experiments and associated numerical simulations.
Monthly Notices of the Royal Astronomical Society, 2013
We analyse the stability and nonlinear dynamical evolution of power-law accretion disc models. Th... more We analyse the stability and nonlinear dynamical evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are strict power-law functions of cylindrical radius, R. We employ two different hydrodynamic codes to perform high resolution 2D-axisymmetric and 3D simulations that examine the long-term evolution of the disc models as a function of the power-law indices of the temperature or entropy, the thermal relaxation time of the fluid, and the disc viscosity. We present an accompanying stability analysis of the problem, based on asymptotic methods, that we use to interpret the results of the simulations. We find that axisymmetric disc models whose temperature or entropy profiles cause the equilibrium angular velocity to vary with height are unstable to the growth of modes with wavenumber ratios |k R /k Z | 1 when the thermodynamic response of the fluid is isothermal, or the thermal evolution time is comparable to or shorter than the local dynamical time scale. These discs are subject to the Goldreich-Schubert-Fricke (GSF) or 'vertical shear' linear instability. Development of the instability involves excitation of vertical breathing and corrugation modes in the disc, with the corrugation modes in particular being a feature of the nonlinear saturated state. Instability is found to operate when the dimensionless disc kinematic viscosity ν < 10 −6 , corresponding to Reynolds numbers Re = Hc s /ν > 2500. In three dimensions the instability generates a quasiturbulent flow, and the associated Reynolds stress produces a fluctuating effective viscosity coefficient whose mean value reaches α ∼ 6 × 10 −4 by the end of the simulation. The evolution and saturation of the vertical shear instability in astrophysical disc models which include realistic treatments of the thermal physics has yet to be examined. Should it occur on either global or local scales, however, our results suggest that it will have significant consequences for their internal dynamics, transport properties, and observational appearance.
Monthly Notices of the Royal Astronomical Society, 2006
The linear normal-mode stratorotational instability (SRI) is analytically reexamined in the invis... more The linear normal-mode stratorotational instability (SRI) is analytically reexamined in the inviscid limit where the length scales of horizontal disturbances are large compared their vertical and radial counterparts. Boundary conditions different than channel walls are also considered. This quasi-hydrostatic, semi-geostrophic (QHSG) approximation allows one to examine the effect of a vertically varying Brunt-Vaisaila frequency, N 2. It is found that the normal-mode instability persists when N 2 increases quadratically with respect to the disc vertical coordinate. However we also find that the SRI seems to exist in this inviscid QHSG extreme only for channel wall conditions: when one or both of the reflecting walls are removed there is no instability in the asymptotic limit explored here. It is also found that only exponential-type SRI modes (as defined by Dubrulle et al. 2005) exist under these conditions. These equations also admit non-normal mode behaviour. Fixed Lagrangian pressure conditions on both radial boundaries predicts there to be no normal mode behaviour in the QHSG limit. The mathematical relationship between the results obtained here and that of the classic Eady (1949) problem for baroclinic instability is drawn. We conjecture as to the mathematical/physical nature of the SRI. The general linear problem, analyzed without approximation in the context of the Boussinesq equations, admits a potential vorticity-like quantity that is advectively conserved by the shear. Its existence means that a continuous spectrum is a generic feature of this system. It also implies that in places where the Brunt-Vaisaila frequency becomes dominant the linearized flow may two-dimensionalize by advectively conserving its vertical vorticity.
Journal of the Atmospheric Sciences, 2008
Motivated by the success of potential vorticity (PV) thinking for Rossby waves and related shear ... more Motivated by the success of potential vorticity (PV) thinking for Rossby waves and related shear flow phenomena, this work develops a buoyancy–vorticity formulation of gravity waves in stratified shear flow, for which the nonlocality enters in the same way as it does for barotropic/baroclinic shear flows. This formulation provides a time integration scheme that is analogous to the time integration of the quasigeostrophic equations with two, rather than one, prognostic equations, and a diagnostic equation for streamfunction through a vorticity inversion. The invertibility of vorticity allows the development of a gravity wave kernel view, which provides a mechanistic rationalization of many aspects of the linear dynamics of stratified shear flow. The resulting kernel formulation is similar to the Rossby-based one obtained for barotropic and baroclinic instability; however, since there are two independent variables—vorticity and buoyancy—there are also two independent kernels at each l...
Journal of Applied Physics, 2008
ABSTRACT Current-voltage relations, electric field, and charge distribution profiles are calculat... more ABSTRACT Current-voltage relations, electric field, and charge distribution profiles are calculated for a device in which the dopants are mobile. The thin film limit is discussed. The model solved is restricted to: (a) mobile holes and acceptors, (b) steady state, and (c) metal electrodes which block the ionic current. The solution is expressed as a series expansion in the small parameter delta=L/lambdaD, where L is the sample thickness and lambdaD is a Debye length. The second order of the series expansion is found to vanish, thus the corrections to the leading order appear only in the third term. The approximated analytic solution agrees with numerical results from a previous publication up to the quite high value of delta=1. The leading order in the I-V relations and in the hole distribution is independent of the acceptor motion. This implies that for thin devices of this form any motion of the dopants may be neglected and that dopants need not be limited only to those which exhibit low diffusion constants. Rectification is observed as long as asymmetry is introduced by two different contact potentials. This holds whether the contacts lead to depletion or accumulation.