COMPACTION AND DENSITY FLUCTUATIONS IN VIBRATED GRANULAR MEDIA

2001 ◽  
Vol 04 (04) ◽  
pp. 389-396
Author(s):  
A. C. B. BARNUM ◽  
ARIF OZBAY ◽  
E. R. NOWAK
Keyword(s):  
Steady State ◽  
Granular Material ◽  
Time Scale ◽  
Granular Media ◽  
Cylindrical Tube ◽  
Density Fluctuations ◽  
Noise Power ◽  
Third Order ◽  
State Densities ◽  
Irreversible Relaxation

We report measurements of the density of a vibrated granular material as a function of time or taps. The material studied consists of monodisperse spherical glass beads confined to a long, thin cylindrical tube. Changes in vibration intensity are used to induce transitions between two steady state densities that depend on the intensity of the vibrations. We find a complex time evolution similar to previous work on the irreversible relaxation from a loose state toward a steady state. In addition, frequency dependent third order moments of the density fluctuations are measured. The data indicate a coupling between large variations in density on one time scale and noise power over a broad range of higher-frequency scales.

Stress fields in granular material and implications for performance of robot locomotion over granular media

2015 ◽  
Vol 8 (1) ◽  
pp. 2005-2009
Author(s):  
Diandong Ren ◽  
Lance M. Leslie ◽  
Congbin Fu
Keyword(s):  
Mechanical Properties ◽  
Granular Material ◽  
Granular Media ◽  
Rotation Frequency ◽  
Legged Locomotion ◽  
Working Environment ◽  
Navier Stokes ◽  
Maximum Speed ◽  
Sigmoid Curve ◽  
Multi Body

 Legged locomotion of robots has advantages in reducing payload in contexts such as travel over deserts or in planet surfaces. A recent study (Li et al. 2013) partially addresses this issue by examining legged locomotion over granular media (GM). However, they miss one extremely significant fact. When the robot’s wheels (legs) run over GM, the granules are set into motion. Hence, unlike the study of Li et al. (2013), the viscosity of the GM must be included to simulate the kinematic energy loss in striking and passing through the GM. Here the locomotion in their experiments is re-examined using an advanced Navier-Stokes framework with a parameterized granular viscosity. It is found that the performance efficiency of a robot, measured by the maximum speed attainable, follows a six-parameter sigmoid curve when plotted against rotating frequency. A correct scaling for the turning point of the sigmoid curve involves the footprint size, rotation frequency and weight of the robot. Our proposed granular response to a load, or the ‘influencing domain’ concept points out that there is no hydrostatic balance within granular material. The balance is a synergic action of multi-body solids. A solid (of whatever density) may stay in equilibrium at an arbitrary depth inside the GM. It is shown that there exists only a minimum set-in depth and there is no maximum or optimal depth. The set-in depth of a moving robot is a combination of its weight, footprint, thrusting/stroking frequency, surface property of the legs against GM with which it has direct contact, and internal mechanical properties of the GM. If the vehicle’s working environment is known, the wheel-granular interaction and the granular mechanical properties can be grouped together. The unitless combination of the other three can form invariants to scale the performance of various designs of wheels/legs. Wider wheel/leg widths increase the maximum achievable speed if all other parameters are unchanged.

Spin down problem of rotating stratified fluid in thermally insulated circular cylinders

1969 ◽  
Vol 37 (4) ◽  
pp. 689-699 ◽  
Author(s):  
Takeo Sakurai
Keyword(s):  
Steady State ◽  
Time Scale ◽  
Boussinesq Approximation ◽  
Circular Cylinders ◽  
Heat Conducting ◽  
Quasi Steady State ◽  
Homogeneous Fluid ◽  
Time Duration ◽  
Viscous Heat ◽  
Final Approach

A response of viscous heat-conducting compressible fluid to an abrupt change of angular velocity of a containing thermally insulated circular cylinder under the existence of stable distribution of the temperature is investigated within the framework of the Boussinesq approximation for a time duration of the order of the homogeneous-fluid spin down time in order to resolve the Holton-Pedlosky controversy. The explicit expression of the solution is obtained by the standard method and Holton's conclusion is confirmed. The secondary meridional current induced by the Ekman layers spins the fluid down to a quasi-steady state within the present time scale. However, unlike the homogeneous case, the quasi-steady state is not one of solid body rotation. The final approach to the state of rigid rotation is achieved via the viscous diffusion in the time scale of the usual diffusion time.

scholarly journals A Duality Approach to Queues with Service Restrictions and Storage Systems with State-Dependent Rates

2013 ◽  
Vol 50 (3) ◽  
pp. 612-631 ◽  
Author(s):  
D. Perry ◽  
W. Stadje ◽  
S. Zacks
Keyword(s):  
Steady State ◽  
Storage Systems ◽  
Storage System ◽  
Queueing Systems ◽  
Local Maxima ◽  
State Dependent ◽  
State Densities ◽  
Duality Approach ◽  
And Storage ◽  
Level Process

Based on pathwise duality constructions, several new results on truncated queues and storage systems of the G/M/1 type are derived by transforming the workload (content) processes into certain ‘dual’ M/G/1-type processes. We consider queueing systems in which (a) any service requirement that would increase the total workload beyond the capacity is truncated so as to keep the associated sojourn time below a certain constant, or (b) new arrivals do not enter the system if they have to wait more than one time unit in line. For these systems, we derive the steady-state distributions of the workload and the numbers of customers present in the systems as well as the distributions of the lengths of busy and idle periods. Moreover, we use the duality approach to study finite capacity storage systems with general state-dependent outflow rates. Here our duality leads to a Markovian finite storage system with state-dependent jump sizes whose content level process can be analyzed using level crossing techniques. We also derive a connection between the steady-state densities of the non-Markovian continuous-time content level process of the G/M/1 finite storage system with state-dependent outflow rule and the corresponding embedded sequence of peak points (local maxima).

A New Simple Non Linear Modelling of the Quasi Statics of Granular Media: predictions, comparisons with experiments

2000 ◽  
Vol 627 ◽  
Author(s):  
Pierre Evesque
Keyword(s):  
Granular Material ◽  
Granular Media ◽  
Stress Ratio ◽  
Rheological Behaviour ◽  
Stress Strain ◽  
Linear Modelling ◽  
Non Linear ◽  
Strain Paths ◽  
Contact Distribution

ABSTRACTFirst, a non linear incremental modelling is proposed to describe rheological behaviour of granular material under different simple (i.e. triaxial-, oedometric-, undrained-) stress-strain paths. Validity of isotropic-response assumption is demonstrated whatever the stress ratio as far as deformation range remains small (ε1<5%). This contradicts some recent hypothesis made on the evolution of contact distribution during anisotropic loading.

A simple composite time scale model for third-order scalar transports

1986 ◽  
Vol 29 (12) ◽  
pp. 3914 ◽  
Author(s):  
Myung Kyoon Chung ◽  
Nam Ho Kyong
Keyword(s):  
Time Scale ◽  
Scale Model ◽  
Third Order
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