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Papers by Norbert Hoffmann
Physical Mesomechanics
ABSTRACT This work presents a model and simulation results for the friction detachment of a finit... more ABSTRACT This work presents a model and simulation results for the friction detachment of a finite sized interface, following previous results on the phenomenon by Ben-David and Fineberg, namely experiments demonstrating that the ratio of shear to normal force needed to move contacting bodies can, instead, vary systematically with controllable changes in the external loading configuration. In particular, we extend a previous one-dimensional simulation model by Bar Sinai with colleagues to a quasi 2D model to allow for a tilting of one of the contacting blocks. While Bar Sinai with colleagues postulate that the presence of slow fronts of detachment (an order of magnitude lower than the usual Rayleigh fronts as in crack propagation) is due to a strengthening term in the friction law, which is not always measured in unlubricated contacts, we find slow fronts also with a purely weakening law.
Scientific reports, Jan 31, 2017
There are two main approximate theories in the contact of rough solids: Greenwood-Williamson aspe... more There are two main approximate theories in the contact of rough solids: Greenwood-Williamson asperity theories (GW) and Persson theories. Neither of them has been fully assessed so far with respect to load-separation curves. Focusing on the most important case of low fractal dimension (D f = 2.2) with extensive numerical studies we find that: (i) Persson's theory describes well the regime of intermediate pressures/contact area, but requires significant corrective factors: the latter depend also on upper wavevector cutoff of the roughness; hence, (ii) Persson's theory does not predict the correct functional dependence on magnification; (iii) asperity theories in the discrete version even neglecting interaction effects are more appropriate in the range of relatively large separations, also to take into consideration of the large scatter in actual realization of the surface.
Wear
A system consisting of a two-degree-of-freedom oscillator with sliding interfaces to two surfaces... more A system consisting of a two-degree-of-freedom oscillator with sliding interfaces to two surfaces subjected to wear is investigated with respect to surface evolution and wear pattern dynamics. The system shows the usual possibility of wear pattern generation due to instabilities of the surface evolution equations. As a novel phenomenon in the context of wear pattern dynamics it is shown that, depending on initial conditions, transient growth of surface properties is possible even in the case of linear stability of the surface evolution. An explanation of the effect is given in terms of non-orthogonality of the surface evolution modes. The effect is to be expected in technical applications with multiple surfaces subjected to wear, like, e.g. friction brakes, and could be regarded as an additional mechanism leading to the generation of surface properties due to wear pattern dynamics.
New Journal of Physics
This work presents an analysis of ocean wave data including rogue waves. A stochastic approach ba... more This work presents an analysis of ocean wave data including rogue waves. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of the scale dependent complexity of ocean waves by means of a Fokker-Planck equation, providing stochastic information of multi-scale processes. In particular we show evidence of Markov properties for increment processes, which means that a three point closure for the complexity of the wave structures seems to be valid. Furthermore we estimate the parameters of the Fokker-Planck equation by parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction. This work presents a new approach where the coherent structure of rogue waves seems to be integrated into the fundamental statistics of complex wave states.
European Journal of Mechanics - B/Fluids
The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogu... more The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogue waves on the ocean caused by nonlinear focusing, is analyzed by direct numerical simulations based on two-phase Navier-Stokes equations. A finite-volume approach with a volume of fluid method is applied to study the Peregrine breather dynamics up to the initial stages of wave breaking. The comparison of the numerical results with laboratory experiments to validate the numerical approach shows very good agreement and suggests that the chosen method is an effective tool to study modulation instability and breather dynamics in water waves with high accuracy even up to the onset of wave breaking. The numerical results also indicate some previously unnoticed characteristics of the flow fields below the water surface of breathers, which might be of significance for short-term prediction of rogue waves. Recurrent wave breaking is also observed.
Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering
Physical Review X
Super rogue waves with an amplitude of up to 5 times the background value are observed in a water... more Super rogue waves with an amplitude of up to 5 times the background value are observed in a waterwave tank for the first time. Nonlinear focusing of the local wave amplitude occurs according to the higher-order breather solution of the nonlinear wave equation. The present result shows that rogue waves can also develop from very calm and apparently safe sea states. We expect the result to have a significant impact on studies of extreme ocean waves and to initiate related studies in other disciplines concerned with waves in nonlinear dispersive media, such as optics, plasma physics, and superfluidity.
Springer Proceedings in Physics, 2009
ABSTRACT
Dokladi Na B Lgarskata Akademiâ Na Naukite, 2009
SAE Technical Paper Series, 2008
... File Size: 109K. Product Status: In Stock See papers presented at 26th Brake Colloquium and E... more ... File Size: 109K. Product Status: In Stock See papers presented at 26th Brake Colloquium and Exhibition, October 2008, San Antonio, TX, USA, Session:Friction-Induced Vibration. Purchase more technical papers and save! With ...
PAMM, 2011
The Ekman-Couette-System consists of two infinitely extended plates which are sheared in opposite... more The Ekman-Couette-System consists of two infinitely extended plates which are sheared in opposite directions over a fluid and are additionally rotated about their normal axis. In the case of angular velocities which tend to zero, the system becomes the classical Couette-System, whereas for high angular velocities the boundary layers of the upper and lower plate are separated and represent Ekman boundary layers. For both limit cases the influence of thermal stratification on the stability of the base flow has been a subject of research for some time, but not so for moderate angular velocities. This was the motivation for doing a linear stability analysis for that case, including both stable and unstable stratification for a Prandtl number equal to unity. The results show, that as expected, stable stratification is suppressing the emergence of stationary as well as Type Iand Type II-shear-instabilities, while unstable stratification is supporting them. For unstable stratification, the system can also become unstable to a convection instability with all its properties known from other systems, except for that their orientation angle is not coincidental but determined due to the influence of the shear and Coriolis forces.
Volume 2: CFD and VIV, 2014
Chaos, Solitons & Fractals, 2014
We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), a... more We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), and multi-fractal detrended fluctuation analysis (MFDFA), for investigating characteristics of vibration time series data from a friction brake. SSA and PCA are used to study the long timescale characteristics of the time series. MFDFA is applied for investigating all time scales up to the smallest recorded one. It turns out that the majority of the long timescale dynamics, that is presumably dominated by the structural dynamics of the brake system, is dominated by very few active dimensions only and can well be understood in terms of low dimensional chaotic attractors. The multifractal analysis shows that the fast dynamical processes originating in the friction interface are in turn truly multi-scale in nature.
Physical Mesomechanics
ABSTRACT This work presents a model and simulation results for the friction detachment of a finit... more ABSTRACT This work presents a model and simulation results for the friction detachment of a finite sized interface, following previous results on the phenomenon by Ben-David and Fineberg, namely experiments demonstrating that the ratio of shear to normal force needed to move contacting bodies can, instead, vary systematically with controllable changes in the external loading configuration. In particular, we extend a previous one-dimensional simulation model by Bar Sinai with colleagues to a quasi 2D model to allow for a tilting of one of the contacting blocks. While Bar Sinai with colleagues postulate that the presence of slow fronts of detachment (an order of magnitude lower than the usual Rayleigh fronts as in crack propagation) is due to a strengthening term in the friction law, which is not always measured in unlubricated contacts, we find slow fronts also with a purely weakening law.
Scientific reports, Jan 31, 2017
There are two main approximate theories in the contact of rough solids: Greenwood-Williamson aspe... more There are two main approximate theories in the contact of rough solids: Greenwood-Williamson asperity theories (GW) and Persson theories. Neither of them has been fully assessed so far with respect to load-separation curves. Focusing on the most important case of low fractal dimension (D f = 2.2) with extensive numerical studies we find that: (i) Persson's theory describes well the regime of intermediate pressures/contact area, but requires significant corrective factors: the latter depend also on upper wavevector cutoff of the roughness; hence, (ii) Persson's theory does not predict the correct functional dependence on magnification; (iii) asperity theories in the discrete version even neglecting interaction effects are more appropriate in the range of relatively large separations, also to take into consideration of the large scatter in actual realization of the surface.
Wear
A system consisting of a two-degree-of-freedom oscillator with sliding interfaces to two surfaces... more A system consisting of a two-degree-of-freedom oscillator with sliding interfaces to two surfaces subjected to wear is investigated with respect to surface evolution and wear pattern dynamics. The system shows the usual possibility of wear pattern generation due to instabilities of the surface evolution equations. As a novel phenomenon in the context of wear pattern dynamics it is shown that, depending on initial conditions, transient growth of surface properties is possible even in the case of linear stability of the surface evolution. An explanation of the effect is given in terms of non-orthogonality of the surface evolution modes. The effect is to be expected in technical applications with multiple surfaces subjected to wear, like, e.g. friction brakes, and could be regarded as an additional mechanism leading to the generation of surface properties due to wear pattern dynamics.
New Journal of Physics
This work presents an analysis of ocean wave data including rogue waves. A stochastic approach ba... more This work presents an analysis of ocean wave data including rogue waves. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of the scale dependent complexity of ocean waves by means of a Fokker-Planck equation, providing stochastic information of multi-scale processes. In particular we show evidence of Markov properties for increment processes, which means that a three point closure for the complexity of the wave structures seems to be valid. Furthermore we estimate the parameters of the Fokker-Planck equation by parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction. This work presents a new approach where the coherent structure of rogue waves seems to be integrated into the fundamental statistics of complex wave states.
European Journal of Mechanics - B/Fluids
The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogu... more The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogue waves on the ocean caused by nonlinear focusing, is analyzed by direct numerical simulations based on two-phase Navier-Stokes equations. A finite-volume approach with a volume of fluid method is applied to study the Peregrine breather dynamics up to the initial stages of wave breaking. The comparison of the numerical results with laboratory experiments to validate the numerical approach shows very good agreement and suggests that the chosen method is an effective tool to study modulation instability and breather dynamics in water waves with high accuracy even up to the onset of wave breaking. The numerical results also indicate some previously unnoticed characteristics of the flow fields below the water surface of breathers, which might be of significance for short-term prediction of rogue waves. Recurrent wave breaking is also observed.
Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering
Physical Review X
Super rogue waves with an amplitude of up to 5 times the background value are observed in a water... more Super rogue waves with an amplitude of up to 5 times the background value are observed in a waterwave tank for the first time. Nonlinear focusing of the local wave amplitude occurs according to the higher-order breather solution of the nonlinear wave equation. The present result shows that rogue waves can also develop from very calm and apparently safe sea states. We expect the result to have a significant impact on studies of extreme ocean waves and to initiate related studies in other disciplines concerned with waves in nonlinear dispersive media, such as optics, plasma physics, and superfluidity.
Springer Proceedings in Physics, 2009
ABSTRACT
Dokladi Na B Lgarskata Akademiâ Na Naukite, 2009
SAE Technical Paper Series, 2008
... File Size: 109K. Product Status: In Stock See papers presented at 26th Brake Colloquium and E... more ... File Size: 109K. Product Status: In Stock See papers presented at 26th Brake Colloquium and Exhibition, October 2008, San Antonio, TX, USA, Session:Friction-Induced Vibration. Purchase more technical papers and save! With ...
PAMM, 2011
The Ekman-Couette-System consists of two infinitely extended plates which are sheared in opposite... more The Ekman-Couette-System consists of two infinitely extended plates which are sheared in opposite directions over a fluid and are additionally rotated about their normal axis. In the case of angular velocities which tend to zero, the system becomes the classical Couette-System, whereas for high angular velocities the boundary layers of the upper and lower plate are separated and represent Ekman boundary layers. For both limit cases the influence of thermal stratification on the stability of the base flow has been a subject of research for some time, but not so for moderate angular velocities. This was the motivation for doing a linear stability analysis for that case, including both stable and unstable stratification for a Prandtl number equal to unity. The results show, that as expected, stable stratification is suppressing the emergence of stationary as well as Type Iand Type II-shear-instabilities, while unstable stratification is supporting them. For unstable stratification, the system can also become unstable to a convection instability with all its properties known from other systems, except for that their orientation angle is not coincidental but determined due to the influence of the shear and Coriolis forces.
Volume 2: CFD and VIV, 2014
Chaos, Solitons & Fractals, 2014
We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), a... more We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), and multi-fractal detrended fluctuation analysis (MFDFA), for investigating characteristics of vibration time series data from a friction brake. SSA and PCA are used to study the long timescale characteristics of the time series. MFDFA is applied for investigating all time scales up to the smallest recorded one. It turns out that the majority of the long timescale dynamics, that is presumably dominated by the structural dynamics of the brake system, is dominated by very few active dimensions only and can well be understood in terms of low dimensional chaotic attractors. The multifractal analysis shows that the fast dynamical processes originating in the friction interface are in turn truly multi-scale in nature.