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Papers by Joseph Rudnick
Physical review letters, Jan 4, 2002
A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a ... more A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a continuously varying order parameter as a transfer matrix calculation allows for the application of methods based on the density matrix renormalization group (DMRG) to the calculation of the free energy of the O(1) model. The essence of both the mapping and the DMRG calculation is laid out, along with results that validate this strategy.
The Journal of the Acoustical Society of America, 1989
The Boltzmann-Ehrenfest principle of adiabatic invariance relates the acoustic potential acting o... more The Boltzmann-Ehrenfest principle of adiabatic invariance relates the acoustic potential acting on a sample positioned in a single-mode cavity to the shift in resonant frequency caused by the presence of this sample. This general and simple relation applies to samples and cavities of arbitrary shape, dimension, and compressibility. Positioning forces and torques can, therefore, be determined from straightforward measurements of frequency shifts. Applications to the Rayleigh disk phenomenon and levitated cylinders are presented.
Eprint Arxiv Cond Mat 0612131, Dec 1, 2006
We explore various properties of classical one-dimensional Wigner solids in the presence of disor... more We explore various properties of classical one-dimensional Wigner solids in the presence of disorder at T=0 in the context of a recently discovered Anderson transition of plasma modes in the random potential system. The extent to which the Wigner lattice is really a ``crystal'' rather than an amorphous solid is discussed for two types of disorder. We investigate the way in which zero point quantum fluctuations that would normally destroy the long range positional order are affected by the disorder. The probability density of particle spacings is examined analytically within a weak disorder approximation and compared to numerical calculations for two different realizations of disorder. We also discuss the multifractal character of the eigenmodes, the compressibility of the electrons, and the AC conductivity.
Phys Rev Lett, 1975
Renormalization-group recursion relations are used to calculate to order ɛ=4-d the free-energy, o... more Renormalization-group recursion relations are used to calculate to order ɛ=4-d the free-energy, ordering-susceptibility, and magnetization-crossover scaling functions for tricritical points in isotropic n-vector models. The equations of state describe critical and tricritical behavior in both ordered and disordered phases.
Physical Review Letters, Jul 23, 2010
We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions... more We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlevé τIV[n] function in the n→0 limit. The large-N thermodynamics exactly recovers that of Kosterlitz, Thouless, and Jones [Phys. Rev. Lett. 36, 1217 (1976)PRLTAO0031-900710.1103/PhysRevLett.36.1217]. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.
We explore various aspects of classical 1D Wigner solids in the presence of strong disorder at T=... more We explore various aspects of classical 1D Wigner solids in the presence of strong disorder at T=0. Two different realizations of electrostatic randomness are studied: a system of particles with spatially random charge strengths and a system of like charges interacting with an external random potential. In the random potential system we have discovered a novel type of vibrational delocalization transition of the plasma oscillations. Finite size scaling studies of the localization length and inverse participation ratio reveal an Anderson transition from extended to localized eigenmodes at larger eigenfrequencies. Other properties of the eigenmodes are also discussed in the context of this criticality. Additionally, for both models the probability density of particle spacings is examined analytically through the use of probability convolutions within a weak disorder approximation and compared to numerically relaxed ensembles. We find that the statistical configuration of the charges is sensitive to the to the specific type of quenched random distribution.
Physical Review B, 1976
Equations of state and renormalization-group recursion relations. Joseph Rudnick Department of Ph... more Equations of state and renormalization-group recursion relations. Joseph Rudnick Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106. ...
Physical Review E, 1999
Domains and bubbles in tilted phases of Langmuir monolayers contain a class of textures known as ... more Domains and bubbles in tilted phases of Langmuir monolayers contain a class of textures known as boojums. The boundaries of such domains and bubbles may display either cusplike features or indentations. We derive analytic expressions for the textures within domains and surrounding bubbles, and for the shapes of the boundaries of these regions. The derivation is perturbative in the deviation of the bounding curve from a circle. This method is not expected to be accurate when the boundary suffers large distortions, but it does provide important clues with regard to the influence of various energetic terms on the order-parameter texture and the shape of the domain or bubble bounding curve. We also look into the effects of thermal fluctuations, which include a sample-size-dependent effective line tension.
Physical Review E, 2000
A numerical algorithm based on the finite element method has been developed to accurately determi... more A numerical algorithm based on the finite element method has been developed to accurately determine the shape of the boundary of a domain containing "boojum" textures, which are order-parameter distributions that resemble the structure of the orbital angular momentum in a superfluid 3He droplet [N.D. Mermin, in Quantum Fluids and Solids, edited by S.B. Trickey, E. Adams, and J.Duffy (Plenum, New York, 1997)]. Within the context of the simple model we adopt, the effects of both bulk elastic anisotropy and line-tension anisotropy on the domain boundary can be examined. It is found that line-tension anisotropy must be present in order to account for domains with protruding features. Both elastic anisotropy and anisotropic line tension can result in domains with indentations. The numerical algorithm has been extended to investigate the problem of a bubble in an extended region ordered phase.
Physics Letters A, 1974
The chemical potential of superfluid condensation is calculated within the Gross-Ginzburg-Pitaevs... more The chemical potential of superfluid condensation is calculated within the Gross-Ginzburg-Pitaevskii theory. There results an expression which is a new relation between pressure and film thickness; the effect on third sound propagation is outlined.
Physical Review Letters, 1981
The effect of external noise on the transition to chaos for maps of the interval which exhibit pe... more The effect of external noise on the transition to chaos for maps of the interval which exhibit period-doubling bifurcations are considered. It is shown that the Liapunov characteristic exponent satisfies scaling in the vicinity of the transition. The critical exponent for noise is calculated with the use of Feigenbaum's renormalization group approach, and the scaling function for the Liapunov characteristic exponent is obtained numerically by iterating a map with additive noise.
Physical Review Letters, 1981
ABSTRACT
Physical Review Letters, 1974
ABSTRACT We reconsider the flow of a superfluid through the interstices of a porous medium, takin... more ABSTRACT We reconsider the flow of a superfluid through the interstices of a porous medium, taking account of the finite volume of the grains and the resulting hydrodynamic drag. A correction factor to the velocity of fourth sound is found, which reconciles a long-standing discrepancy between theory and experiment.
Physical Review Letters, 2010
We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions... more We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlevé τ{IV}[n] function in the n→0 limit. The large-N thermodynamics exactly recovers that of Kosterlitz, Thouless, and Jones [Phys. Rev. Lett. 36, 1217 (1976)10.1103/PhysRevLett.36.1217]. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.
Physical Review Letters, 2007
The destruction of quasi-long-range crystalline order as a consequence of strong disorder effects... more The destruction of quasi-long-range crystalline order as a consequence of strong disorder effects is shown to accompany the strict localization of all classical plasma modes of one-dimensional Wigner crystals at T=0. We construct a phase diagram that relates the structural phase properties of Wigner crystals to a plasmon delocalization transition recently reported. Deep inside the strictly localized phase of the strong disorder regime, we observe glasslike behavior. However, well into the critical phase with a plasmon mobility edge, the system retains its crystalline composition. We predict that a transition between the two phases occurs at a critical value of the relative disorder strength. This transition has an experimental signature in the ac conductivity as a local maximum of the largest spectral amplitude as a function of the relative disorder strength.
Physical Review E, 2013
We study elasticity-driven morphological transitions of soft spherical core-shell structures in w... more We study elasticity-driven morphological transitions of soft spherical core-shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response is dominated by bending. To generate the transitions, we consider the case where the surface area of the liquid layer is increased for a fixed amount of interior elastic material. We find that generically there is a critical excess surface area at which the isotropic sphere becomes unstable to buckling. At this point it adopts a lower symmetry wrinkled structure that can be described by a spherical harmonic deformation. We study the dependence of the buckled sphere and critical excess area of the transition on the elastic parameters and size of the system. We also relate our results to recent experiments on the wrinkling of gel-filled vesicles as their interior volume is reduced. The theory may have broader applications to a variety of related structures from the macroscopic to the microscopic, including the wrinkling of dried peas, raisins, as well as the cell nucleus.
Physical Review E, 2008
We discuss the effects of external stress on the thermal denaturation of homogeneous DNA. Pulling... more We discuss the effects of external stress on the thermal denaturation of homogeneous DNA. Pulling double-stranded DNA at each end exerts a profound effect on the thermal denaturation, or melting, of a long segment of this molecule. We discuss the effects on this transition of a stretching force applied to opposite ends of the DNA, including full consideration of the consequences of excluded volume, the analysis of which is greatly simplified in this case. We find that in three dimensions the heat capacity acquires a logarithmic dependence on reduced temperature.
Physical Review B, 2007
We explore various properties of classical one-dimensional Wigner solids in the presence of weak ... more We explore various properties of classical one-dimensional Wigner solids in the presence of weak disorder at T=0 in the context of a recently discovered Anderson transition of plasma modes in a random potential system. The extent to which the Wigner lattice is really a ``crystal'' rather than an amorphous solid is discussed for two types of disorder. The probability density of particle spacings is examined analytically within a weak disorder approximation and compared to numerical calculations for two different realizations of disorder. Regarding the plasma oscillations, the exact plasmon dispersion relations for the ordered Wigner crystal is derived analytically from the real space equations of motion. The methods introduced for performing the necessary lattice sums can be extended to tight-binding models of noninteracting electrons with power law hopping. We also discuss other quantities that follow from plasma oscillations such as the multifractal eigenfunctions, the compressibility of the electrons, and the ac conductivity.
The Journal of the Acoustical Society of America, 1991
A method is described for use with an acoustic positioner, which enables a determination of the e... more A method is described for use with an acoustic positioner, which enables a determination of the equilibrium position and orientation which an object assumes in a zero gravity environment, as well as restoring forces and torques of an object in an acoustic standing wave field. An acoustic standing wave field is established in the chamber, and the object is held at several different positions near the expected equilibrium position. While the object is held at each position, the center resonant frequency of the chamber is determined, by noting which frequency results in the greatest pressure of the acoustic field. The object position which results in the lowest center resonant frequency is the equilibrium position. The orientation of a nonspherical object is similarly determined, by holding the object in a plurality of different orientations at its equilibrium position, and noting the center resonant frequency for each orientation. The orientation which results in the lowest center resonant frequency is the equilibrium orientation. Where the acoustic frequency is constant, but the chamber length is variable, the equilibrium position or orientation is that which results in the greatest chamber length at the center resonant frequency.
Physical review letters, Jan 4, 2002
A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a ... more A formulation of the Ginzburg-Landau-Wilson version of the partition function of a system with a continuously varying order parameter as a transfer matrix calculation allows for the application of methods based on the density matrix renormalization group (DMRG) to the calculation of the free energy of the O(1) model. The essence of both the mapping and the DMRG calculation is laid out, along with results that validate this strategy.
The Journal of the Acoustical Society of America, 1989
The Boltzmann-Ehrenfest principle of adiabatic invariance relates the acoustic potential acting o... more The Boltzmann-Ehrenfest principle of adiabatic invariance relates the acoustic potential acting on a sample positioned in a single-mode cavity to the shift in resonant frequency caused by the presence of this sample. This general and simple relation applies to samples and cavities of arbitrary shape, dimension, and compressibility. Positioning forces and torques can, therefore, be determined from straightforward measurements of frequency shifts. Applications to the Rayleigh disk phenomenon and levitated cylinders are presented.
Eprint Arxiv Cond Mat 0612131, Dec 1, 2006
We explore various properties of classical one-dimensional Wigner solids in the presence of disor... more We explore various properties of classical one-dimensional Wigner solids in the presence of disorder at T=0 in the context of a recently discovered Anderson transition of plasma modes in the random potential system. The extent to which the Wigner lattice is really a ``crystal'' rather than an amorphous solid is discussed for two types of disorder. We investigate the way in which zero point quantum fluctuations that would normally destroy the long range positional order are affected by the disorder. The probability density of particle spacings is examined analytically within a weak disorder approximation and compared to numerical calculations for two different realizations of disorder. We also discuss the multifractal character of the eigenmodes, the compressibility of the electrons, and the AC conductivity.
Phys Rev Lett, 1975
Renormalization-group recursion relations are used to calculate to order ɛ=4-d the free-energy, o... more Renormalization-group recursion relations are used to calculate to order ɛ=4-d the free-energy, ordering-susceptibility, and magnetization-crossover scaling functions for tricritical points in isotropic n-vector models. The equations of state describe critical and tricritical behavior in both ordered and disordered phases.
Physical Review Letters, Jul 23, 2010
We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions... more We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlevé τIV[n] function in the n→0 limit. The large-N thermodynamics exactly recovers that of Kosterlitz, Thouless, and Jones [Phys. Rev. Lett. 36, 1217 (1976)PRLTAO0031-900710.1103/PhysRevLett.36.1217]. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.
We explore various aspects of classical 1D Wigner solids in the presence of strong disorder at T=... more We explore various aspects of classical 1D Wigner solids in the presence of strong disorder at T=0. Two different realizations of electrostatic randomness are studied: a system of particles with spatially random charge strengths and a system of like charges interacting with an external random potential. In the random potential system we have discovered a novel type of vibrational delocalization transition of the plasma oscillations. Finite size scaling studies of the localization length and inverse participation ratio reveal an Anderson transition from extended to localized eigenmodes at larger eigenfrequencies. Other properties of the eigenmodes are also discussed in the context of this criticality. Additionally, for both models the probability density of particle spacings is examined analytically through the use of probability convolutions within a weak disorder approximation and compared to numerically relaxed ensembles. We find that the statistical configuration of the charges is sensitive to the to the specific type of quenched random distribution.
Physical Review B, 1976
Equations of state and renormalization-group recursion relations. Joseph Rudnick Department of Ph... more Equations of state and renormalization-group recursion relations. Joseph Rudnick Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106. ...
Physical Review E, 1999
Domains and bubbles in tilted phases of Langmuir monolayers contain a class of textures known as ... more Domains and bubbles in tilted phases of Langmuir monolayers contain a class of textures known as boojums. The boundaries of such domains and bubbles may display either cusplike features or indentations. We derive analytic expressions for the textures within domains and surrounding bubbles, and for the shapes of the boundaries of these regions. The derivation is perturbative in the deviation of the bounding curve from a circle. This method is not expected to be accurate when the boundary suffers large distortions, but it does provide important clues with regard to the influence of various energetic terms on the order-parameter texture and the shape of the domain or bubble bounding curve. We also look into the effects of thermal fluctuations, which include a sample-size-dependent effective line tension.
Physical Review E, 2000
A numerical algorithm based on the finite element method has been developed to accurately determi... more A numerical algorithm based on the finite element method has been developed to accurately determine the shape of the boundary of a domain containing "boojum" textures, which are order-parameter distributions that resemble the structure of the orbital angular momentum in a superfluid 3He droplet [N.D. Mermin, in Quantum Fluids and Solids, edited by S.B. Trickey, E. Adams, and J.Duffy (Plenum, New York, 1997)]. Within the context of the simple model we adopt, the effects of both bulk elastic anisotropy and line-tension anisotropy on the domain boundary can be examined. It is found that line-tension anisotropy must be present in order to account for domains with protruding features. Both elastic anisotropy and anisotropic line tension can result in domains with indentations. The numerical algorithm has been extended to investigate the problem of a bubble in an extended region ordered phase.
Physics Letters A, 1974
The chemical potential of superfluid condensation is calculated within the Gross-Ginzburg-Pitaevs... more The chemical potential of superfluid condensation is calculated within the Gross-Ginzburg-Pitaevskii theory. There results an expression which is a new relation between pressure and film thickness; the effect on third sound propagation is outlined.
Physical Review Letters, 1981
The effect of external noise on the transition to chaos for maps of the interval which exhibit pe... more The effect of external noise on the transition to chaos for maps of the interval which exhibit period-doubling bifurcations are considered. It is shown that the Liapunov characteristic exponent satisfies scaling in the vicinity of the transition. The critical exponent for noise is calculated with the use of Feigenbaum's renormalization group approach, and the scaling function for the Liapunov characteristic exponent is obtained numerically by iterating a map with additive noise.
Physical Review Letters, 1981
ABSTRACT
Physical Review Letters, 1974
ABSTRACT We reconsider the flow of a superfluid through the interstices of a porous medium, takin... more ABSTRACT We reconsider the flow of a superfluid through the interstices of a porous medium, taking account of the finite volume of the grains and the resulting hydrodynamic drag. A correction factor to the velocity of fourth sound is found, which reconciles a long-standing discrepancy between theory and experiment.
Physical Review Letters, 2010
We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions... more We present an alternate solution of a Gaussian spin-glass model with infinite ranged interactions and a global spherical constraint at zero magnetic field. The replicated spin-glass Hamiltonian is mapped onto a Coulomb gas of logarithmically interacting particles confined by a logarithmic single particle potential. The precise free energy is obtained by analyzing the Painlevé τ{IV}[n] function in the n→0 limit. The large-N thermodynamics exactly recovers that of Kosterlitz, Thouless, and Jones [Phys. Rev. Lett. 36, 1217 (1976)10.1103/PhysRevLett.36.1217]. It is hoped that the approach here can be extended to apply to systems beyond the spherical model, particularly those in which destabilizing terms lead to replica symmetry breaking.
Physical Review Letters, 2007
The destruction of quasi-long-range crystalline order as a consequence of strong disorder effects... more The destruction of quasi-long-range crystalline order as a consequence of strong disorder effects is shown to accompany the strict localization of all classical plasma modes of one-dimensional Wigner crystals at T=0. We construct a phase diagram that relates the structural phase properties of Wigner crystals to a plasmon delocalization transition recently reported. Deep inside the strictly localized phase of the strong disorder regime, we observe glasslike behavior. However, well into the critical phase with a plasmon mobility edge, the system retains its crystalline composition. We predict that a transition between the two phases occurs at a critical value of the relative disorder strength. This transition has an experimental signature in the ac conductivity as a local maximum of the largest spectral amplitude as a function of the relative disorder strength.
Physical Review E, 2013
We study elasticity-driven morphological transitions of soft spherical core-shell structures in w... more We study elasticity-driven morphological transitions of soft spherical core-shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response is dominated by bending. To generate the transitions, we consider the case where the surface area of the liquid layer is increased for a fixed amount of interior elastic material. We find that generically there is a critical excess surface area at which the isotropic sphere becomes unstable to buckling. At this point it adopts a lower symmetry wrinkled structure that can be described by a spherical harmonic deformation. We study the dependence of the buckled sphere and critical excess area of the transition on the elastic parameters and size of the system. We also relate our results to recent experiments on the wrinkling of gel-filled vesicles as their interior volume is reduced. The theory may have broader applications to a variety of related structures from the macroscopic to the microscopic, including the wrinkling of dried peas, raisins, as well as the cell nucleus.
Physical Review E, 2008
We discuss the effects of external stress on the thermal denaturation of homogeneous DNA. Pulling... more We discuss the effects of external stress on the thermal denaturation of homogeneous DNA. Pulling double-stranded DNA at each end exerts a profound effect on the thermal denaturation, or melting, of a long segment of this molecule. We discuss the effects on this transition of a stretching force applied to opposite ends of the DNA, including full consideration of the consequences of excluded volume, the analysis of which is greatly simplified in this case. We find that in three dimensions the heat capacity acquires a logarithmic dependence on reduced temperature.
Physical Review B, 2007
We explore various properties of classical one-dimensional Wigner solids in the presence of weak ... more We explore various properties of classical one-dimensional Wigner solids in the presence of weak disorder at T=0 in the context of a recently discovered Anderson transition of plasma modes in a random potential system. The extent to which the Wigner lattice is really a ``crystal'' rather than an amorphous solid is discussed for two types of disorder. The probability density of particle spacings is examined analytically within a weak disorder approximation and compared to numerical calculations for two different realizations of disorder. Regarding the plasma oscillations, the exact plasmon dispersion relations for the ordered Wigner crystal is derived analytically from the real space equations of motion. The methods introduced for performing the necessary lattice sums can be extended to tight-binding models of noninteracting electrons with power law hopping. We also discuss other quantities that follow from plasma oscillations such as the multifractal eigenfunctions, the compressibility of the electrons, and the ac conductivity.
The Journal of the Acoustical Society of America, 1991
A method is described for use with an acoustic positioner, which enables a determination of the e... more A method is described for use with an acoustic positioner, which enables a determination of the equilibrium position and orientation which an object assumes in a zero gravity environment, as well as restoring forces and torques of an object in an acoustic standing wave field. An acoustic standing wave field is established in the chamber, and the object is held at several different positions near the expected equilibrium position. While the object is held at each position, the center resonant frequency of the chamber is determined, by noting which frequency results in the greatest pressure of the acoustic field. The object position which results in the lowest center resonant frequency is the equilibrium position. The orientation of a nonspherical object is similarly determined, by holding the object in a plurality of different orientations at its equilibrium position, and noting the center resonant frequency for each orientation. The orientation which results in the lowest center resonant frequency is the equilibrium orientation. Where the acoustic frequency is constant, but the chamber length is variable, the equilibrium position or orientation is that which results in the greatest chamber length at the center resonant frequency.