scholarly journals Temporal variations in rockfall and rock-wall retreat rates in a deglaciated valley over the past 11 k.y.

Geology ◽  
2020 ◽  
Vol 48 (6) ◽  
pp. 594-598 ◽  
Author(s):  
Solmaz Mohadjer ◽  
Todd A. Ehlers ◽  
Matthias Nettesheim ◽  
Marco B. Ott ◽  
Christoph Glotzbach ◽  
...  
Keyword(s):  
Power Law ◽  
Time Scale ◽  
Temporal Variations ◽  
Climatic Conditions ◽  
Short Time Scale ◽  
Similar Frequency ◽  
Rock Wall ◽  
Significant Difference ◽  
Long Time ◽  
Frequency Magnitude

Abstract This study addresses the temporal variations in rockfall activity in the 5.2 km2 calcareous cliffs of the deglaciated Lauterbrunnen Valley, Switzerland. We did this using 19 campaigns of repeated terrestrial laser scans (TLS) over 5.2 yr, power-law predicted behavior from extrapolation of the TLS-derived frequency-magnitude relationship, and estimates of long-time-scale (∼11 k.y.) activity based on the volume of preserved postglacial rockfall talus. Results from the short-time-scale observations indicate no statistically significant difference between TLS observations averaging over 1.5 versus 5.2 yr. Rock-wall retreat rates in both cases are 0.03–0.08 mm/yr. In contrast, the power-law predicted rock-wall retreat rates are 0.14–0.22 mm/yr, and long-term rates from talus volumes are 0.27–0.38 mm/yr. These results suggest (1) short (1.5 yr) TLS inventories of rockfalls provide (within uncertainties) similar frequency-magnitude relationships as longer (5.2 yr) inventories, thereby suggesting short observation periods may be sufficient for hazard characterization from TLS, and (2) higher rock-wall retreat rates over long time scales (Holocene averaged) may reflect debuttressing and stress relaxation effects after glacial retreat, and/or enhanced rockfall activity under periglacial (climatic) conditions.

scholarly journals Stratified Flows over and around Long Dynamically Tall Mountain Ridges

2019 ◽  
Vol 76 (5) ◽  
pp. 1265-1287 ◽  
Author(s):  
Arjun Jagannathan ◽  
Kraig Winters ◽  
Laurence Armi
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Stratified Flows ◽  
Half Width ◽  
Short Time Scale ◽  
Late Time ◽  
Low Level ◽  
Long Time ◽  
Flow Splitting ◽  
Short Time

Abstract Uniformly stratified flows approaching long and dynamically tall ridges develop two distinct flow components over disparate time scales. The fluid upstream and below a “blocking level” is stagnant in the limit of an infinite ridge and flows around the sides when the ridge extent is finite. The streamwise half-width of the obstacle at the blocking level arises as a natural inner length scale for the flow, while the excursion time over this half-width is an associated short time scale for the streamwise flow evolution. Over a longer time scale, low-level horizontal flow splitting leads to the establishment of an upstream layerwise potential flow beneath the blocking level. We demonstrate through numerical experiments that for sufficiently long ridges, crest control and streamwise asymmetry are seen on both the short and long time scales. On the short time scale, upstream blocking is established quickly and the flow is well described as a purely infinite-ridge overflow. Over the long time scale associated with flow splitting, low-level flow escapes around the sides, but the overflow continues to be hydraulically controlled and streamwise asymmetric in the neighborhood of the crest. We quantify this late-time overflow by estimating its volumetric transport and then briefly demonstrate how this approach can be extended to predict the overflow across nonuniform ridge shapes.

Structural derivative based on inverse Mittag-Leffler function for modeling ultraslow diffusion

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Wen Chen ◽  
Yingjie Liang ◽  
Xindong Hei
Keyword(s):  
Diffusion Model ◽  
Time Scale ◽  
Structural Function ◽  
Short Time Scale ◽  
Mathematical Tool ◽  
Interacting Particles ◽  
Random System ◽  
Ballistic Motion ◽  
Time Space ◽  
Long Time

AbstractThis paper proposes a novel structural derivative approach to tackle the perplexing modeling problem of ultraslow diffusion. The structural function plays a central role in this new strategy as a kernel transform of underlying time-space fabric of physical systems. Ultraslow diffusion has been observed in numerous lab experiments and field observations, whose behaviors deviate dramatically from the standard anomalous diffusion models characterizing power function of time. The logarithmic diffusion model has since been used to describe bizarre process of ultraslow diffusion but with very limited success. This study applies the inverse Mittag-Leffler function as the structural function in the structural derivative modeling ultraslow diffusion of a random system of two interacting particles. It is observed that the dynamics of two interacting particles are respectively the ballistic motion at the short time scale and the Sinai ultraslow diffusion at the long time scale. Compared with the logarithmic diffusion model, the inverse Mittag-Leffler diffusion model has higher accuracy and manifests clearer physical mechanism. Numerical experiments show that the structural derivative is a feasible mathematical tool to model the ultraslow diffusion using the inverse Mittag-Leffler function as its structural function.

On Failure Mechanisms in Flip Chip Assembly—Part 2: Optimal Underfill and Interconnecting Materials

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Yoonchan Oh ◽  
C. Steve Suh ◽  
Hung-Jue Sue
Keyword(s):  
Time Scale ◽  
Flip Chip ◽  
Thermal Stresses ◽  
Failure Modes ◽  
Scale Effects ◽  
Short Time Scale ◽  
Long Time ◽  
Solder Joint Fatigue ◽  
Scale Properties ◽  
Short Time

The physics explored in this investigation enables short-time scale dynamic phenomenon to be correlated with package failure modes such as solder ball cracking and interlayer debond. It is found that although epoxy-based underfills with nanofillers are shown to be effective in alleviating thermal stresses and improving solder joint fatigue performance in thermal cycling tests of long-time scale, underfill material viscoelasticity is ineffective in attenuating short-time scale propagating shock waves. In addition, the inclusion of Cu interconnecting layers in flip chip area arrays is found to perform significantly better than Al layers in suppressing short-time scale effects. Results reported herein suggest that, if improved flip chip reliability is to be achieved, the compositions of all packaging constituent materials need be formulated to have well-defined short-time scale and long-time scale properties. Chip level circuit design layout also needs be optimized to either discourage or negate short-time wave propagation. The knowledge base established is generally applicable to high performance package configurations of small footprint and high clock speed. The approach along with the numerical procedures developed for the investigation can be a practical tool for realizing better device reliability and thus high manufacturing yield.

scholarly journals Mathematical modelling and application of frog choruses as an autonomous distributed communication system

2019 ◽  
Vol 6 (1) ◽  
pp. 181117 ◽  
Author(s):  
Ikkyu Aihara ◽  
Daichi Kominami ◽  
Yasuharu Hirano ◽  
Masayuki Murata
Keyword(s):  
Mathematical Model ◽  
Wireless Sensor Network ◽  
Mathematical Modelling ◽  
Sensor Network ◽  
Time Scale ◽  
Wireless Sensor ◽  
Multiple Time Scales ◽  
Short Time Scale ◽  
Long Time ◽  
Short Time

Interactions using various sensory cues produce sophisticated behaviour in animal swarms, e.g. the foraging behaviour of ants and the flocking of birds and fish. Here, we investigate the behavioural mechanisms of frog choruses from the viewpoints of mathematical modelling and its application. Empirical data on male Japanese tree frogs demonstrate that (1) neighbouring male frogs avoid call overlaps with each other over a short time scale and (2) they collectively switch between the calling state and the silent state over a long time scale. To reproduce these features, we propose a mathematical model in which separate dynamical models spontaneously switch due to a stochastic process depending on the internal dynamics of respective frogs and also the interactions among the frogs. Next, the mathematical model is applied to the control of a wireless sensor network in which multiple sensor nodes send a data packet towards their neighbours so as to deliver the packet to a gateway node by multi-hop communication. Numerical simulation demonstrates that (1) neighbouring nodes can avoid a packet collision over a short time scale by alternating the timing of data transmission and (2) all the nodes collectively switch their states over a long time scale, establishing high network connectivity while reducing network power consumption. Consequently, this study highlights the unique dynamics of frog choruses over multiple time scales and also provides a novel bio-inspired technology that is applicable to the control of a wireless sensor network.

scholarly journals Sliding of spherical ball on solid lubricating coating combined with wear process

2021 ◽  
Vol 93 (1) ◽  
pp. 39-50
Author(s):  
Marcin Białas ◽  
Jan Maciejewski ◽  
Stanisław Kucharski
Keyword(s):  
Steady State ◽  
Time Scale ◽  
Contact Region ◽  
Short Time Scale ◽  
Steady State Condition ◽  
Wear Process ◽  
Spherical Ball ◽  
Long Time ◽  
Short Time ◽  
Solid Lubricating Coating

In present paper we show results of ball-on-disk wear experiment of MoS2 film deposited on Ti6Al4V substrate. The ball materials is aluminum oxide. The tests are performed for different surrounding temperature conditions: 20 oC, 200 oC and 350 oC. It is shown that depth of the wear groove increases with increasing surrounding temperature. A finite element modeling approach is next developed to mimic the experimental observations of ball-on-disk wear process. It is based on the assumption of steady state condition developed during short time scale at contact region. The steady state results can next be applied to long time scale in which wear process is numerically simulated. Model results are compared with experimentally obtained wear groove and show satisfactory agreement.

scholarly journals The Mathematical Analysis On The Effect Of Strong Nonlinearity On Steady-State Self-Focusing And Filamentation Of Whistlers In A Plasma

2016 ◽  
Vol 5 (1) ◽  
pp. 18
Author(s):  
Ghanshyam Rai
Keyword(s):  
Time Scale ◽  
High Frequency ◽  
Small Scale ◽  
Nonuniform Heating ◽  
Short Time Scale ◽  
Strong Nonlinearity ◽  
Self Focusing ◽  
Long Time ◽  
Short Time ◽  
Very High

<div><p><em>A high-power Gaussian Whistler propagating in a magnatoplasma becomes self-focused because of (i) ponderomotive force and (ii) nonuniform heating nonlinearities (i) being dominant for t &lt;&lt; T and (ii) being dominant for t &gt; t<sub>E</sub>. On short time scale (t &lt;&lt; t<sub>E</sub> ) whistlers of all frequencies can be focused (the self – focusing length is very large for ω= </em><em> /2 and decreases rapidly on both sides), whereas on the long time scale (t &gt; t<sub>E</sub>) only high frequency whistlers (ω&gt; </em><em> /2) are focused. At very high powers the plasma is depleted almost completely from the axial region and self-focusing does not occur, rather, defocusing takes place. </em></p><p><em>            A plane uniform whistler of high intensity is seen to be unstable for small scale fluctuations, i.e., it must break up into filaments in course of it propagation. The growth rate increases with decreasing scale length of perturbation and is seen to be a saturating function of power density of the beam. </em></p></div>

scholarly journals The effects of driving time scales on heating in a coronal arcade

2020 ◽  
Vol 643 ◽  
pp. A85
Author(s):  
T. A. Howson ◽  
I. De Moortel ◽  
L. E. Fyfe
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Time Scales ◽  
Time Scale ◽  
Plasma Temperature ◽  
Short Time Scale ◽  
Heating Rates ◽  
Poynting Flux ◽  
Long Time

Context. The relative importance of alternating current (AC) and direct current (DC) heating mechanisms in maintaining the temperature of the solar corona is not well constrained. Aims. We aim to investigate the effects of the characteristic time scales of photospheric driving on the injection and dissipation of magnetic and kinetic energy within a coronal arcade. Methods. We conducted three-dimensional magnetohydrodynamic simulations of complex foot point driving imposed on a potential coronal arcade. We modified the typical time scales associated with the velocity driver to understand the efficiency of heating obtained using AC and DC drivers. We considered the implications for the injected Poynting flux and the spatial and temporal nature of the energy release in dissipative regimes. Results. For the same driver amplitude and complexity, long time scale velocity motions are able to inject a much greater Poynting flux of energy into the corona. Consequently, in non-ideal regimes, slow stressing motions result in a greater increase in plasma temperature than for wave-like driving. In dissipative simulations, Ohmic heating is found to be much more significant than viscous heating. For all drivers in our parameter space, energy dissipation is greatest close to the base of the arcade, where the magnetic field strength is strongest, and at separatrix surfaces, where the field connectivity changes. Across all simulations, the background field is stressed with random foot point motions (in a manner more typical of DC heating studies), and, even for short time scale driving, the injected Poynting flux is large given the small amplitude flows considered. For long time scale driving, the rate of energy injection was comparable to the expected requirements in active regions. The heating rates were found to scale with the perturbed magnetic field strength and not the total field strength. Conclusions. Alongside recent studies that show that power within the corona is dominated by low frequency motions, our results suggest that, in the closed corona, DC heating is more significant than AC heating.

scholarly journals Investigating the route to flutter in a pitch-plunge airfoil with freeplay nonlinearity subjected to input flow fluctuations

2018 ◽  
Vol 211 ◽  
pp. 02012
Author(s):  
R Magu Raam Prasaad ◽  
J Venkatramani
Keyword(s):  
Time Scale ◽  
Mean Value ◽  
Dynamical Behaviour ◽  
Short Time Scale ◽  
Input Flow ◽  
Response Dynamics ◽  
Aeroelastic System ◽  
Flow Fluctuations ◽  
Freeplay Nonlinearity ◽  
Long Time

Aeroelastic systems with freeplay nonlinearity can exhibit a wide variety of qualitatively different dynamical responses such as limit cycle oscillations and chaos in the pre-flutter regimes. Consequently, the bifurcation scenario in an aeroelastic system with freeplay nonlinearity under uniform flows have received considerable attention in the literature. However, in reality flows are far from deterministic and often possess a small temporal random fluctuations about a mean value. Input flow fluctuations have the potential to alter the stability and give rise to atypical routes to flutter. Indeed, recent studies have shown that under flow fluctuations the aeroelastic systems loses its stability via a regime of oscillations called intermittency. Further, it is observed that the presence of cubic hardening nonlinearity and input flow fluctuations with predominantly long time scales can give rise to “on-off” type intermittency. This dynamical behaviour is attributed to type of nonlinearity and relatively short time scale for the system to stay and exhibit distinct dynamics. Extending the mechanism of intermittency route to flutter in aeroelastic systems with other prominent types of nonlinearities, such as, freeplay have however, received minimal attention in the literature. The present study devotes itself to investigate the response dynamics of an airfoil with freeplay nonlinearity subjected to long time scale input flow fluctuations.

scholarly journals Estimation of Soil Respiration by Its Driving Factors Based on Multi-Source Data in a Sub-Alpine Meadow in North China

2019 ◽  
Vol 11 (12) ◽  
pp. 3274 ◽  
Author(s):  
Yanan Liang ◽  
Yanpeng Cai ◽  
Junxia Yan ◽  
Hongjian Li
Keyword(s):  
Remote Sensing ◽  
Soil Respiration ◽  
Seasonal Variations ◽  
Land Surface ◽  
North China ◽  
Alpine Meadow ◽  
Temporal Variations ◽  
Exponential Model ◽  
Climatic Conditions ◽  
Significant Difference

Soil respiration (Rs) in high-altitude areas are normally sensitive to varying climatic conditions. The objective of this research was mainly to explore temporal variations in Rs rates and the corresponding controlling factors for the establishment of appropriate fitting models in a sub-alpine meadow of north China. The data was obtained through field measuring and extraction of the Moderate Resolution Imaging Spectroradiometer (MODIS) in the geographical unit of the study site over the period of 2007 to 2015. The main results were as follows: (1) seasonal variations in Rs rates, soil temperature (Ts), land surface temperature (LST), and normalized difference vegetation index (NDVI) all produced symmetrical bell type patterns, while soil moisture (Ms) showed a fluctuating pattern, (2) a Ts-exponential model could greatly capture seasonal variations of Rs rates in the study site, reflecting the role of temperature as a dominant driving factor in determining Rs temporal variations in alpine meadow areas, (3) there was no significant difference between the performing indicators evaluating the proposed Ts-exponential model and the LST-exponential model. This indicated great potential for applying remote sensing products to estimate seasonal Rs rates and 4) seasonal variations in Rs rates towards temperature sensitivity (Q10) showed a concave curve and dramatically decreased as the temperature increased from −1 to 11 °C. Overall, the results indicated that attention to significant effects of climatic conditions on Rs, particularly in areas of low temperature, should be warranted. Also, applicability of remote sensing products for estimating Rs was reflected and demonstrated.

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