Ulrich Zurcher | Cleveland State University (original) (raw)
Papers by Ulrich Zurcher
A number of studies have evaluated lumbar spinal muscle fatigue using the electromyography (EMG) ... more A number of studies have evaluated lumbar spinal muscle fatigue using the electromyography (EMG) signal. However, back muscle fatigue studies do not consistently report endurance levels for patients with or without low back pain (LBP). In this case report, we investigated a nonlinear analysis of EMG time series that characterizes their complexity
Bulletin of the American Physical Society, 2016
(standing) and dynamic equilibrium (walking). This suggests that sways of the body are important ... more (standing) and dynamic equilibrium (walking). This suggests that sways of the body are important for a person to maintain the upright position and prevent a fall. We examine the center of pressure (COP) changes with visual input, and find that the character of COP dynamics is different on different time scales: it is random (stochastic) on short time scales 0 < t < 20 ms, ballistic (deterministic) on intermediate time scales 20 ms < t < 200 ms, and random on long time scales 200 ms < t < 25 s.
ACS Symposium Series, 1997
Liquids and glasses have localized low-frequency vibrational modes associated with disorder. Thes... more Liquids and glasses have localized low-frequency vibrational modes associated with disorder. These modes represent relaxational motion in double wells, and quasi-harmonic motions in single wells. Single- and double-well potentials are described by the soft-potential model, which is an extension of the two-level-system model for glasses. We use soft modes to derive the unstable frequency spectrum of instantaneous normal modes in liquids. In agreement with recent molecular-dynamics simulations, we find different frequency and temperature dependence of the spectrum for liquids in the normal and supercooled phase. We relate this crossover behavior to the presence of shear stress in the liquid. Assuming that the diffusion of particles requires hopping over potential barriers, we find exponential temperature dependence of the shear viscosity. Arrhenius and Zwanzig-Bässler behavior follows for liquids in the normal and supercooled phase, respectively. We discuss properties of the energy landscape in glass-forming liquids. Possible applications to protein dynamics are mentioned
Complex Variables
Outline The course text is: K. F. Riley & M. P. Hobson: Essential Mathematical Methods (Cambridge... more Outline The course text is: K. F. Riley & M. P. Hobson: Essential Mathematical Methods (Cambridge UP, New York, 2011) [RH] [1]. Two other standard comprehensive texts are [2] [3]. An older text is by Morse and Feshbach from M.I.T. [4]. More "sophisticated" texts include [5]. There are numerous texts that cover special topics. Some of the choices are: [6] for Functional Analysis (Hilbert spaces,...), [7] for real and complex analysis (Hilbert abd Banach spaces, harmonic functions, complex integration,...), [8] for Tensor Analysis, and [9] for group theory. In addition, there are numerous physics texts that contain a fair amount of mathematical methods. Examples are [10] for ordinary and partial differential equations, or [11] for differential geometry. For differential equations, I find Ref. [12] very useful. Finally, [13] is an excellent text on linear algebra. We closely follow RH and students are expected to read the text and follow the examples. Class time is spent sketching the mathematics and discussing examples in detail.
are in the process of assessing the effectiveness of fractal and entropic measures for the diagno... more are in the process of assessing the effectiveness of fractal and entropic measures for the diagnostic of low back pain from surface electromyography (EMG) time series. Surface electromyography (EMG) is used to assess patients with low back pain. In a typical EMG measurement, the voltage is measured every millisecond. We observed back muscle fatiguing during one minute, which results in a time series with 60,000 entries. We characterize the complexity of time series by computing the Shannon entropy time dependence. The analysis of the time series from different relevant muscles from healthy and low back pain (LBP) individuals provides evidence that the level of variability of back muscle activities is much larger for healthy individuals than for individuals with LBP. In general the time dependence of the entropy shows a crossover from a diffusive regime to a regime characterized by long time correlations (self organization) at about 0.01s.
American Journal of Physics
The wave equation of sound is developed starting from the equations of fluid mechanics for the ve... more The wave equation of sound is developed starting from the equations of fluid mechanics for the velocity and pressure variation in air. The equations for sound are analogous to Maxwell's equations for linear polarized electromagnetic plane waves: the pressure variation and the velocity correspond to the electric and magnetic fields, respectively. The order of magnitude of sound properties is explained in terms of the amplitude and energy density of the corresponding wave.
Physical Review E, 1993
We investigate the thermally activated escape of a Brownian particle over a potential barrier who... more We investigate the thermally activated escape of a Brownian particle over a potential barrier whose height fluctuates with a rate o. between the values E+ and E. We are mainly interested in the lowtemperature behavior where E+ /T &)E /T. We calculate the mean exit time as a function of the rate of the barrier fluctuations for the piecewise linear and the piecewise constant barrier,~=~(a). For the piecewise constant potential we find three different regimes:~-~+ for a(~+ =exp(-E+ /T),~-2f or a& w '=exp(-E /T), and w-a ' for~+'(e(w '. The mean exit time for the piecewise linear potential has a different behavior for fast barrier fluctuations, o.)~;~(a) is a monotonously increasing function that approaches the asymptotic value r-Jr+ r for a-+~. We show that the behavior of the mean exit time for the piecewise constant potential is characterized by the absence of correlations between barrier crossings and barrier fluctuations. We discuss these correlations in some detail for the piecewise linear potential barrier.
Arboreal locomotion-traveling on the branches, twigs, and trunks of trees and woody shrubs-is ver... more Arboreal locomotion-traveling on the branches, twigs, and trunks of trees and woody shrubs-is very common among mammals. Most primates, many rodents, marsupials, carnivores, and even an occasional artiodactyl travel on arboreal substrates to forage, escape predators, and acquire shelter. Arboreal supports are usually far enough from the ground that a slip or fall could cause serious injury or death, or deprive the animal of a mate, food, or energy. Thus, stability is of great importance for an animal traveling on arboreal supports. The considerable variation among arboreal supports makes stability during locomotion a mechanical challenge. Supports vary in diameter, slope, compliance, texture, direction (that is, bends or curves in a branch), and number and distribution. Furthermore there may be interaction among these variables; for example, compliance varies with diameter-thinner branches are more compliant than thick branches. Also, the thin branches frequently have leaves that act like sails in the wind, causing even more movement in the substrate. Substrate texture often varies with diameter, where narrow twigs have smoother bark than large branches or trunks. Therefore one might expect a considerable number of morphological, behavioral, and biomechanical mechanisms to enhance stability on arboreal supports. Stability can be divided into two categories: static and dynamic. Static stability is the process by which objects at rest remain stable, i.e., neither move (translation) nor rotate about a point or axis. For example, a table is statically stable because the forces and moments (torques) produced by gravity (weight) are balanced by ground reaction forces and the moments generated by them. One way an animal might remain stable is by not moving and adhering to or gripping the support; this definition is the ultimate example of static stability in an animal. Although this strategy allows no movement, it is nevertheless a valid locomotor strategy for an animal attempting to travel on an arboreal support subjected to a sudden gust of wind or other disturbance (Stevens, 2003). This analysis also applies when the animal walks very slowly, but fails when it walks or runs at considerable speed. Because the distribution of the mass is changing from one instant to the next, the forces and torques necessary to maintain static stability would also change with time. That is, it requires an active control by the nervous system. Because stability is critical, it is very likely that the animal employs both active and passive control (Full et al., 2002). Passive control can be due to dynamic processes of the animal's body, and is referred to as dynamic stability. For example, a hiker might cross a stream or river by running across a fallen log; the rotation of the limbs around the hips and shoulder
Bulletin of the American Physical Society, 2014
discuss a Huygens' model in the "language" for someone with a background in algebra-based physics... more discuss a Huygens' model in the "language" for someone with a background in algebra-based physics. The system consists of two pendulums mounted on a cart. We show how the movement of the cart removes the degeneracy of the two bobs, and use the conservation of linear momentum to describe the necessary escapement mechanism. We present results from an Excel calculation for the decay of the symmetric and antisymmetric modes.
to the quantum quartic oscillator are not known. We equip the set of Hamiltonian operators with a... more to the quantum quartic oscillator are not known. We equip the set of Hamiltonian operators with a metric, thereby providing a notion of distance between these operators. This metric is a generalization of the L 2 metric on the space of Lebesgue measurable functions. We determine Hamiltonian operators with known solutions (to the Scrödinger equation), and then use the generalized metric to find a unique Hamiltonian with known solutions that is minimal in distance to the quartic Hamiltonian. The Hamiltonian that we seek is, in fact, the Hamiltonian of the harmonic oscillator. Minimizing the distance will correspondingly suggest a harmonic frequency. The approximate solutions to the quartic oscillator will thus be the solutions of the harmonic oscillator with the suggested frequency.
Physical Review E, 1999
Soft vibrational modes have been used to explain anomalous thermal properties of glasses above 1 ... more Soft vibrational modes have been used to explain anomalous thermal properties of glasses above 1 K. The soft-potential model consists of a collection of double-well potentials that are distorted by a linear term representing local stress in the liquid. Double-well modes contribute to the configurational entropy of the system. Based on the Adam-Gibbs theory of entropically driven relaxation in liquids, we show that the presence of stress drives the transition from Arrhenius to Zwanzig-Bässler temperature dependence of relaxation times. At some temperature below the glass transition, the energy scale is dominated by local stress, and soft modes are described by single wells only. It follows that the configurational entropy vanishes, in agreement with the ''Kauzmann paradox.'' We discuss a possible connection between soft vibrational modes and ultrafast processes that dominate liquid dynamics near the glass transition. ͓S1063-651X͑99͒12108-1͔
European Journal of Physics, 2016
In molecular systems, positive and negative charges are separated, making them ideal systems to e... more In molecular systems, positive and negative charges are separated, making them ideal systems to examine electrostatic interactions. The attractive force between positive and negative charges is balanced by repulsive 'forces' that are quantum-mechanical in origin. We introduce an 'effective' potential energy that captures the repulsion; it allows us to obtain fairly accurate estimates of the bonding properties of molecular systems. We use units (e.g., kcal mol-1 for energy) that emphasize the relevance of electrostatics to macroscopic behavior.
We have previously reported that the mean-square displacement calculated from electromyography ti... more We have previously reported that the mean-square displacement calculated from electromyography time series of low back muscles exhibit a plateau-like behavior for intermediate times [50 ,ms < t < 0.5 ,s], so that < [xt- x0]^2 > ˜t^0. This behavior is unexpected, and indicates the presence of long-time correlations in the signal. For fractal Brownian motion, the Hurst exponent calculated from the mean-square displacement and the exponent from the spectral density P ( f) ˜1/f^α, α= 2 H + 1. For the EMG time series y^0i= xi, we have generated iterated time series, yi^n+1 = [y2 i ^n + y2i+1]/2, and have calculated the corresponding time correlation functions, C^n ( t) = < xi+ t^n xi^n>/<(xi^n)^2 >. We find that the correlation functions converge to a simple limit, C(0) = 1, C(1) = -0.5 and C(n) =0 for n >=2. This limit is consistent with the plateau behavior of the mean- square displacement. We discuss the connection between the behavior of the iterated correlation functions and the properties of the spectrum.
Aps Ohio Sections Spring Meeting Abstracts, Mar 1, 2006
Key properties of open systems are discussed by using the mechanical analogue of a particle immer... more Key properties of open systems are discussed by using the mechanical analogue of a particle immersed in a fluid. The difference between mechanical and thermal equilibrium is discussed. The material can be used in an algebra-based physics course.
European Journal of Physics, 2016
Particle-wave duality is a central tenet of quantum physics, and an electron has wave-like proper... more Particle-wave duality is a central tenet of quantum physics, and an electron has wave-like properties. Introductory texts discuss the wavelength-momentum relationship l = h p, but do not discuss the frequency-energy relationship. This is curious since a wave is periodic both in space and time. The discussion in more advanced texts is not satisfactory either since two different expressions for the frequency are given based on the relativistic and nonrelativistic expression for the electron energy. The relativistic expression yields the correct frequency, and we explain why the expression based on the Schrödinger equation gives the incorrect expression. We argue that the electron frequency should be discussed at the introductory level.
Many-body theory is used to explain super-Arrhenius behavior of viscous properties of glassformin... more Many-body theory is used to explain super-Arrhenius behavior of viscous properties of glassforming liquids. An elastic theory for supercooled liquids shows that vibrations are described by linear strain, while re-arrangements of cages [groups of atoms] give rise to nonlinear strain. Ignoring the identity of individual particles in the system, we arrive at a description of the system for long times in terms of vibrational degrees of freedom. Re-orientations of cages on mesoscopic timescales are then mimicked by a fluctuating potential. We recover Zwanzig's model for diffusion in a rough potential [PNAS 85, 2029 (1988)]. Super-Arrhenius behavior is shown to imply that the shift in the potential energy is a local symmetry. This requires the presence of a ``gauge'' field which we identify with stress in the liquid. We propose a free energy for stress.
Configurational diffusion dynamics of proteins has been described by diffusion in a rough energy ... more Configurational diffusion dynamics of proteins has been described by diffusion in a rough energy landscape [R. Zwanzig, PNAS 85, 2029 (1988)]. In the model, the potential energy V(x) has a smooth and rough component V(x) = V0 (x) + V_1(x) where the rougness at different coordinates are uncorrelated <V1 (x) V1 ( x') > = 0. Zwanzig assumed a Gaussian statistics for the rougness and derived super-Arrhenius behavior of the mean-first-passage time, t =t0 exp ( [ɛ/k T]^2), where T is the temperature and ɛ is the variance of the rougness ɛ^2 = < V_1^2 >. We re-examine this model and show that the model implies a non-zero force along the one-dimensional coordinate which we identify with long-range stress in the system. The force can be interpreted as an order parameter, and we derive an expression for the free energy.
Zoology (Jena, Germany), 2011
When animals travel on tree branches, avoiding falls is of paramount importance. Animals swiftly ... more When animals travel on tree branches, avoiding falls is of paramount importance. Animals swiftly running on a narrow branch must rely on movement to create stability rather than on static methods. We examined how Siberian chipmunks (Tamias sibiricus) remain stable while running on a narrow tree branch trackway. We examined the pitch, yaw, and rolling torques around the center of mass, and hypothesized that within a stride, any angular impulse (torque during step time) acting on the center of mass would be canceled out by an equal and opposite angular impulse. Three chipmunks were videotaped while running on a 2cm diameter branch trackway. We digitized the videos to estimate center of mass and center of pressure positions throughout the stride. A short region of the trackway was instrumented to measure components of the substrate reaction force. We found that positive and negative pitch angular impulse was by far the greatest in magnitude. The anterior body was pushed dorsally (upwar...
European Journal of Physics, 2013
A simple experiment for determining the nonlinear stress-strain relation of duct tape is describe... more A simple experiment for determining the nonlinear stress-strain relation of duct tape is described. After weights are added and subsequently removed, the tape does not return to its original state and is no longer taut. The tape exhibits hysteresis, which implies the loss of work during the cyclical process. The exponent describing the nonlinearity is related to the fractional work loss.
A number of studies have evaluated lumbar spinal muscle fatigue using the electromyography (EMG) ... more A number of studies have evaluated lumbar spinal muscle fatigue using the electromyography (EMG) signal. However, back muscle fatigue studies do not consistently report endurance levels for patients with or without low back pain (LBP). In this case report, we investigated a nonlinear analysis of EMG time series that characterizes their complexity
Bulletin of the American Physical Society, 2016
(standing) and dynamic equilibrium (walking). This suggests that sways of the body are important ... more (standing) and dynamic equilibrium (walking). This suggests that sways of the body are important for a person to maintain the upright position and prevent a fall. We examine the center of pressure (COP) changes with visual input, and find that the character of COP dynamics is different on different time scales: it is random (stochastic) on short time scales 0 < t < 20 ms, ballistic (deterministic) on intermediate time scales 20 ms < t < 200 ms, and random on long time scales 200 ms < t < 25 s.
ACS Symposium Series, 1997
Liquids and glasses have localized low-frequency vibrational modes associated with disorder. Thes... more Liquids and glasses have localized low-frequency vibrational modes associated with disorder. These modes represent relaxational motion in double wells, and quasi-harmonic motions in single wells. Single- and double-well potentials are described by the soft-potential model, which is an extension of the two-level-system model for glasses. We use soft modes to derive the unstable frequency spectrum of instantaneous normal modes in liquids. In agreement with recent molecular-dynamics simulations, we find different frequency and temperature dependence of the spectrum for liquids in the normal and supercooled phase. We relate this crossover behavior to the presence of shear stress in the liquid. Assuming that the diffusion of particles requires hopping over potential barriers, we find exponential temperature dependence of the shear viscosity. Arrhenius and Zwanzig-Bässler behavior follows for liquids in the normal and supercooled phase, respectively. We discuss properties of the energy landscape in glass-forming liquids. Possible applications to protein dynamics are mentioned
Complex Variables
Outline The course text is: K. F. Riley & M. P. Hobson: Essential Mathematical Methods (Cambridge... more Outline The course text is: K. F. Riley & M. P. Hobson: Essential Mathematical Methods (Cambridge UP, New York, 2011) [RH] [1]. Two other standard comprehensive texts are [2] [3]. An older text is by Morse and Feshbach from M.I.T. [4]. More "sophisticated" texts include [5]. There are numerous texts that cover special topics. Some of the choices are: [6] for Functional Analysis (Hilbert spaces,...), [7] for real and complex analysis (Hilbert abd Banach spaces, harmonic functions, complex integration,...), [8] for Tensor Analysis, and [9] for group theory. In addition, there are numerous physics texts that contain a fair amount of mathematical methods. Examples are [10] for ordinary and partial differential equations, or [11] for differential geometry. For differential equations, I find Ref. [12] very useful. Finally, [13] is an excellent text on linear algebra. We closely follow RH and students are expected to read the text and follow the examples. Class time is spent sketching the mathematics and discussing examples in detail.
are in the process of assessing the effectiveness of fractal and entropic measures for the diagno... more are in the process of assessing the effectiveness of fractal and entropic measures for the diagnostic of low back pain from surface electromyography (EMG) time series. Surface electromyography (EMG) is used to assess patients with low back pain. In a typical EMG measurement, the voltage is measured every millisecond. We observed back muscle fatiguing during one minute, which results in a time series with 60,000 entries. We characterize the complexity of time series by computing the Shannon entropy time dependence. The analysis of the time series from different relevant muscles from healthy and low back pain (LBP) individuals provides evidence that the level of variability of back muscle activities is much larger for healthy individuals than for individuals with LBP. In general the time dependence of the entropy shows a crossover from a diffusive regime to a regime characterized by long time correlations (self organization) at about 0.01s.
American Journal of Physics
The wave equation of sound is developed starting from the equations of fluid mechanics for the ve... more The wave equation of sound is developed starting from the equations of fluid mechanics for the velocity and pressure variation in air. The equations for sound are analogous to Maxwell's equations for linear polarized electromagnetic plane waves: the pressure variation and the velocity correspond to the electric and magnetic fields, respectively. The order of magnitude of sound properties is explained in terms of the amplitude and energy density of the corresponding wave.
Physical Review E, 1993
We investigate the thermally activated escape of a Brownian particle over a potential barrier who... more We investigate the thermally activated escape of a Brownian particle over a potential barrier whose height fluctuates with a rate o. between the values E+ and E. We are mainly interested in the lowtemperature behavior where E+ /T &)E /T. We calculate the mean exit time as a function of the rate of the barrier fluctuations for the piecewise linear and the piecewise constant barrier,~=~(a). For the piecewise constant potential we find three different regimes:~-~+ for a(~+ =exp(-E+ /T),~-2f or a& w '=exp(-E /T), and w-a ' for~+'(e(w '. The mean exit time for the piecewise linear potential has a different behavior for fast barrier fluctuations, o.)~;~(a) is a monotonously increasing function that approaches the asymptotic value r-Jr+ r for a-+~. We show that the behavior of the mean exit time for the piecewise constant potential is characterized by the absence of correlations between barrier crossings and barrier fluctuations. We discuss these correlations in some detail for the piecewise linear potential barrier.
Arboreal locomotion-traveling on the branches, twigs, and trunks of trees and woody shrubs-is ver... more Arboreal locomotion-traveling on the branches, twigs, and trunks of trees and woody shrubs-is very common among mammals. Most primates, many rodents, marsupials, carnivores, and even an occasional artiodactyl travel on arboreal substrates to forage, escape predators, and acquire shelter. Arboreal supports are usually far enough from the ground that a slip or fall could cause serious injury or death, or deprive the animal of a mate, food, or energy. Thus, stability is of great importance for an animal traveling on arboreal supports. The considerable variation among arboreal supports makes stability during locomotion a mechanical challenge. Supports vary in diameter, slope, compliance, texture, direction (that is, bends or curves in a branch), and number and distribution. Furthermore there may be interaction among these variables; for example, compliance varies with diameter-thinner branches are more compliant than thick branches. Also, the thin branches frequently have leaves that act like sails in the wind, causing even more movement in the substrate. Substrate texture often varies with diameter, where narrow twigs have smoother bark than large branches or trunks. Therefore one might expect a considerable number of morphological, behavioral, and biomechanical mechanisms to enhance stability on arboreal supports. Stability can be divided into two categories: static and dynamic. Static stability is the process by which objects at rest remain stable, i.e., neither move (translation) nor rotate about a point or axis. For example, a table is statically stable because the forces and moments (torques) produced by gravity (weight) are balanced by ground reaction forces and the moments generated by them. One way an animal might remain stable is by not moving and adhering to or gripping the support; this definition is the ultimate example of static stability in an animal. Although this strategy allows no movement, it is nevertheless a valid locomotor strategy for an animal attempting to travel on an arboreal support subjected to a sudden gust of wind or other disturbance (Stevens, 2003). This analysis also applies when the animal walks very slowly, but fails when it walks or runs at considerable speed. Because the distribution of the mass is changing from one instant to the next, the forces and torques necessary to maintain static stability would also change with time. That is, it requires an active control by the nervous system. Because stability is critical, it is very likely that the animal employs both active and passive control (Full et al., 2002). Passive control can be due to dynamic processes of the animal's body, and is referred to as dynamic stability. For example, a hiker might cross a stream or river by running across a fallen log; the rotation of the limbs around the hips and shoulder
Bulletin of the American Physical Society, 2014
discuss a Huygens' model in the "language" for someone with a background in algebra-based physics... more discuss a Huygens' model in the "language" for someone with a background in algebra-based physics. The system consists of two pendulums mounted on a cart. We show how the movement of the cart removes the degeneracy of the two bobs, and use the conservation of linear momentum to describe the necessary escapement mechanism. We present results from an Excel calculation for the decay of the symmetric and antisymmetric modes.
to the quantum quartic oscillator are not known. We equip the set of Hamiltonian operators with a... more to the quantum quartic oscillator are not known. We equip the set of Hamiltonian operators with a metric, thereby providing a notion of distance between these operators. This metric is a generalization of the L 2 metric on the space of Lebesgue measurable functions. We determine Hamiltonian operators with known solutions (to the Scrödinger equation), and then use the generalized metric to find a unique Hamiltonian with known solutions that is minimal in distance to the quartic Hamiltonian. The Hamiltonian that we seek is, in fact, the Hamiltonian of the harmonic oscillator. Minimizing the distance will correspondingly suggest a harmonic frequency. The approximate solutions to the quartic oscillator will thus be the solutions of the harmonic oscillator with the suggested frequency.
Physical Review E, 1999
Soft vibrational modes have been used to explain anomalous thermal properties of glasses above 1 ... more Soft vibrational modes have been used to explain anomalous thermal properties of glasses above 1 K. The soft-potential model consists of a collection of double-well potentials that are distorted by a linear term representing local stress in the liquid. Double-well modes contribute to the configurational entropy of the system. Based on the Adam-Gibbs theory of entropically driven relaxation in liquids, we show that the presence of stress drives the transition from Arrhenius to Zwanzig-Bässler temperature dependence of relaxation times. At some temperature below the glass transition, the energy scale is dominated by local stress, and soft modes are described by single wells only. It follows that the configurational entropy vanishes, in agreement with the ''Kauzmann paradox.'' We discuss a possible connection between soft vibrational modes and ultrafast processes that dominate liquid dynamics near the glass transition. ͓S1063-651X͑99͒12108-1͔
European Journal of Physics, 2016
In molecular systems, positive and negative charges are separated, making them ideal systems to e... more In molecular systems, positive and negative charges are separated, making them ideal systems to examine electrostatic interactions. The attractive force between positive and negative charges is balanced by repulsive 'forces' that are quantum-mechanical in origin. We introduce an 'effective' potential energy that captures the repulsion; it allows us to obtain fairly accurate estimates of the bonding properties of molecular systems. We use units (e.g., kcal mol-1 for energy) that emphasize the relevance of electrostatics to macroscopic behavior.
We have previously reported that the mean-square displacement calculated from electromyography ti... more We have previously reported that the mean-square displacement calculated from electromyography time series of low back muscles exhibit a plateau-like behavior for intermediate times [50 ,ms < t < 0.5 ,s], so that < [xt- x0]^2 > ˜t^0. This behavior is unexpected, and indicates the presence of long-time correlations in the signal. For fractal Brownian motion, the Hurst exponent calculated from the mean-square displacement and the exponent from the spectral density P ( f) ˜1/f^α, α= 2 H + 1. For the EMG time series y^0i= xi, we have generated iterated time series, yi^n+1 = [y2 i ^n + y2i+1]/2, and have calculated the corresponding time correlation functions, C^n ( t) = < xi+ t^n xi^n>/<(xi^n)^2 >. We find that the correlation functions converge to a simple limit, C(0) = 1, C(1) = -0.5 and C(n) =0 for n >=2. This limit is consistent with the plateau behavior of the mean- square displacement. We discuss the connection between the behavior of the iterated correlation functions and the properties of the spectrum.
Aps Ohio Sections Spring Meeting Abstracts, Mar 1, 2006
Key properties of open systems are discussed by using the mechanical analogue of a particle immer... more Key properties of open systems are discussed by using the mechanical analogue of a particle immersed in a fluid. The difference between mechanical and thermal equilibrium is discussed. The material can be used in an algebra-based physics course.
European Journal of Physics, 2016
Particle-wave duality is a central tenet of quantum physics, and an electron has wave-like proper... more Particle-wave duality is a central tenet of quantum physics, and an electron has wave-like properties. Introductory texts discuss the wavelength-momentum relationship l = h p, but do not discuss the frequency-energy relationship. This is curious since a wave is periodic both in space and time. The discussion in more advanced texts is not satisfactory either since two different expressions for the frequency are given based on the relativistic and nonrelativistic expression for the electron energy. The relativistic expression yields the correct frequency, and we explain why the expression based on the Schrödinger equation gives the incorrect expression. We argue that the electron frequency should be discussed at the introductory level.
Many-body theory is used to explain super-Arrhenius behavior of viscous properties of glassformin... more Many-body theory is used to explain super-Arrhenius behavior of viscous properties of glassforming liquids. An elastic theory for supercooled liquids shows that vibrations are described by linear strain, while re-arrangements of cages [groups of atoms] give rise to nonlinear strain. Ignoring the identity of individual particles in the system, we arrive at a description of the system for long times in terms of vibrational degrees of freedom. Re-orientations of cages on mesoscopic timescales are then mimicked by a fluctuating potential. We recover Zwanzig's model for diffusion in a rough potential [PNAS 85, 2029 (1988)]. Super-Arrhenius behavior is shown to imply that the shift in the potential energy is a local symmetry. This requires the presence of a ``gauge'' field which we identify with stress in the liquid. We propose a free energy for stress.
Configurational diffusion dynamics of proteins has been described by diffusion in a rough energy ... more Configurational diffusion dynamics of proteins has been described by diffusion in a rough energy landscape [R. Zwanzig, PNAS 85, 2029 (1988)]. In the model, the potential energy V(x) has a smooth and rough component V(x) = V0 (x) + V_1(x) where the rougness at different coordinates are uncorrelated <V1 (x) V1 ( x') > = 0. Zwanzig assumed a Gaussian statistics for the rougness and derived super-Arrhenius behavior of the mean-first-passage time, t =t0 exp ( [ɛ/k T]^2), where T is the temperature and ɛ is the variance of the rougness ɛ^2 = < V_1^2 >. We re-examine this model and show that the model implies a non-zero force along the one-dimensional coordinate which we identify with long-range stress in the system. The force can be interpreted as an order parameter, and we derive an expression for the free energy.
Zoology (Jena, Germany), 2011
When animals travel on tree branches, avoiding falls is of paramount importance. Animals swiftly ... more When animals travel on tree branches, avoiding falls is of paramount importance. Animals swiftly running on a narrow branch must rely on movement to create stability rather than on static methods. We examined how Siberian chipmunks (Tamias sibiricus) remain stable while running on a narrow tree branch trackway. We examined the pitch, yaw, and rolling torques around the center of mass, and hypothesized that within a stride, any angular impulse (torque during step time) acting on the center of mass would be canceled out by an equal and opposite angular impulse. Three chipmunks were videotaped while running on a 2cm diameter branch trackway. We digitized the videos to estimate center of mass and center of pressure positions throughout the stride. A short region of the trackway was instrumented to measure components of the substrate reaction force. We found that positive and negative pitch angular impulse was by far the greatest in magnitude. The anterior body was pushed dorsally (upwar...
European Journal of Physics, 2013
A simple experiment for determining the nonlinear stress-strain relation of duct tape is describe... more A simple experiment for determining the nonlinear stress-strain relation of duct tape is described. After weights are added and subsequently removed, the tape does not return to its original state and is no longer taut. The tape exhibits hysteresis, which implies the loss of work during the cyclical process. The exponent describing the nonlinearity is related to the fractional work loss.