scholarly journals Scaling ansatz for the jamming transition

2016 ◽  
Vol 113 (35) ◽  
pp. 9745-9750 ◽  
Author(s):  
Carl P. Goodrich ◽  
Andrea J. Liu ◽  
James P. Sethna
Keyword(s):  
Shear Stress ◽  
Compressive Strain ◽  
System Size ◽  
Renormalization Group Theory ◽  
Scaling Exponents ◽  
Jamming Transition ◽  
Potential Development ◽  
Residual Shear Stress ◽  
Theoretical Results ◽  
Insight Into

We propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.

scholarly journals Regulation of the normalized rate of driven magnetic reconnection through shocked flux pileup

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Joseph Olson ◽  
Jan Egedal ◽  
Michael Clark ◽  
Douglass A. Endrizzi ◽  
Samuel Greess ◽  
...  
Keyword(s):  
Magnetic Reconnection ◽  
System Size ◽  
Force Balance ◽  
Absolute Rate ◽  
Reconnection Rate ◽  
Supersonic Plasma ◽  
Reconnection Layer ◽  
Inflow Conditions ◽  
Theoretical Results

Magnetic reconnection is explored on the Terrestrial Reconnection Experiment (TREX) for asymmetric inflow conditions and in a configuration where the absolute rate of reconnection is set by an external drive. Magnetic pileup enhances the upstream magnetic field of the high-density inflow, leading to an increased upstream Alfvén speed and helping to lower the normalized reconnection rate to values expected from theoretical consideration. In addition, a shock interface between the far upstream supersonic plasma inflow and the region of magnetic flux pileup is observed, important to the overall force balance of the system, thereby demonstrating the role of shock formation for configurations including a supersonically driven inflow. Despite the specialized geometry where a strong reconnection drive is applied from only one side of the reconnection layer, previous numerical and theoretical results remain robust and are shown to accurately predict the normalized rate of reconnection for the range of system sizes considered. This experimental rate of reconnection is dependent on system size, reaching values as high as 0.8 at the smallest normalized system size applied.

ChunkSim

2010 ◽  
pp. 131-149
Author(s):  
Pedro Furtado
Keyword(s):  
Performance Analysis ◽  
Simulation Analysis ◽  
System Size ◽  
Analysis Tool ◽  
Data Allocation ◽  
Data Warehouses ◽  
Availability Analysis ◽  
On Demand ◽  
Self Tuning ◽  
Insight Into

Self-tuning physical database organization involves tools that determine automatically the best solution concerning partitioning, placement, creation and tuning of auxiliary structures (e.g. indexes), based on the workload. To the best of our knowledge, no tool has focused on a relevant issue in parallel databases and in particular data warehouses running on common off-the-shelf hardware in a sharednothing configuration: determining the adequate tradeoff for balancing load and availability with costs (storage and loading costs). In previous work, we argued that effective load and availability balancing over partitioned datasets can be obtained through chunk-wise placement and replication, together with on-demand processing. In this work, we propose ChunkSim, a simulator for system size planning, performance analysis against replication degree and availability analysis. We apply the tool to illustrate the kind of results that can be obtained by it. The whole discussion in the chapter provides very important insight into data allocation and query processing over shared-nothing data warehouses and how a good simulation analysis tool can be built to predict and analyze actual systems and intended deployments.

Analysis of Traction Curve in Linear Region Considering Volume Viscoelasticity

1999 ◽  
Vol 121 (2) ◽  
pp. 252-258 ◽  
Author(s):  
Narihiko Yoshimura ◽  
Noboru Umemoto ◽  
Tsunamitsu Nakahara
Keyword(s):  
High Pressure ◽  
Shear Stress ◽  
High Speed ◽  
Viscoelastic Model ◽  
Primary Data ◽  
Elastic Model ◽  
Linear Region ◽  
Slip Ratio ◽  
Traction Test ◽  
Theoretical Results

Measurements of the gradient in the linear region of traction curve, where the effects of heat generation and nonlinearity of shear viscosity can be neglected were made for two kinds of synthetic oils, DOP and 5P4E, using a traction tester improved to a precision less than 0.01 percent in slip ratio. The measured results were compared with the theoretical results based on a viscoelastic model for shear stress and on an elastic model for compressibility using primary data of the rheological properties which were obtained not by means of traction test; they were markedly less than the theoretical results under low speed for both oils and also under high speed for DOP. A new analysis of the traction was performed considering volume viscoelasticity for compressibility which relates shear viscoelasticity under high pressure. The theoretical results agree fairly with the measured results.

LIGHT-INDUCED MODIFICATION OF KINETIC MOLECULAR PROPERTIES: ENHANCEMENT OF OPTICAL KERR EFFECT IN ABSORBING LIQUIDS, PHOTOINDUCED TORQUE AND MOLECULAR MOTORS IN DYE-DOPED NEMATICS

2000 ◽  
Vol 09 (02) ◽  
pp. 157-182 ◽  
Author(s):  
M. KREUZER ◽  
L. MARRUCCI ◽  
D. PAPARO
Keyword(s):  
Liquid Crystals ◽  
Molecular Motors ◽  
Kerr Effect ◽  
Optical Nonlinearity ◽  
Molecular Structures ◽  
Molecular Properties ◽  
Main Role ◽  
Theoretical Results ◽  
Insight Into ◽  
Dye Molecule

In this paper we review some experimental and theoretical results on the enhancement of orientational optical nonlinearities observed in dye-doped liquids and liquid crystals. We argue that this enhancement is derived from a photoinduced modification of kinetic molecular properties. Moreover we highlight an analogy between the mechanism of this effect in nematic liquid crystals and the working principles of "molecular motors". This analogy helps us to refine the understanding of this effect and to identify the molecular parameters which play the main role. Finally we review some recent experimental results about the dependence of the optical nonlinearity enhancement on the detailed dye and host molecular structures. These results provide some insight into the light-induced phenomena taking place inside a dye molecule.

A Theoretical Investigation of the Jet-Flap Compressor Cascade in Incompressible Flow

1972 ◽  
Vol 94 (4) ◽  
pp. 249-260
Author(s):  
U. Stark
Keyword(s):  
Incompressible Flow ◽  
Time Pressure ◽  
Inviscid Flow ◽  
Compressor Cascade ◽  
Pressure Distributions ◽  
Simplifying Assumptions ◽  
Stagger Angle ◽  
First Time ◽  
Theoretical Results ◽  
Insight Into

The use of jet flaps gives a new possibility of achieving high turning cascades. In this paper a new theory for unstaggered cascades with jet flaps, developed under simplifying assumptions, is described. With the help of this theory, besides turning angles and lift coefficients, for the first time pressure distributions on, and jet slope distributions behind, the blades were calculated. The effect of stagger angle on the turning angles and lift coefficients is determined with the help of the Schlichting method, using the concept of the equivalent flat plate cascade. Sample calculations illustrate the theory and, at the same time, give an insight into the behavior of cascades with jet flaps in inviscid flow. Results of previously published experiments on cascades with jet flaps, where they fulfill the conditions of the theory, are compared with the theoretical results and demonstrate satisfactory agreement.

Structural and energy insights on solid-state complexes with trimethoprim: a combined theoretical and experimental investigation

2015 ◽  
Vol 71 (4) ◽  
pp. 406-415
Author(s):  
Anaelle Tilborg ◽  
Andrea Carletta ◽  
Johan Wouters
Keyword(s):  
Organic Salt ◽  
X Ray Diffraction ◽  
Torsion Angles ◽  
Conformational Studies ◽  
X Ray ◽  
Hydrogen Bond Interactions ◽  
Structural Database ◽  
Theoretical Results ◽  
Insight Into ◽  
Good Agreement

We present here a new structure of a 1:1 salt of trimethoprim with hemifumarate, highlighted by single-crystal X-ray diffraction and computational conformational studies. This salt was formed during cocrystallization assays conducted to combine trimethoprim and other APIs whose combination exhibits interesting properties. Theoreticalin vacuoinvestigations have been performed on the organic salt through a DFT two-dimensional conformational scan of torsion angles between the two aromatic moieties of trimethoprim. The evaluation of relative energies for hydrogen-bond interactions in the structure has also been performed. Comparison with conformational data from structures implying trimethoprim retrieved from the Cambridge Structural Database (CSD) shows good agreement with theoretical results, proving the validity of vacuumab initiocalculations in describing the energetic landscape of the molecule and thereby gain initial insight into the prediction process for possible new conformations and therefore potential new polymorphs.

UV Raman Spectroscopy Study of Strain Induced by Buried Silicon Nitride Layer in the BOX of Silicon On Insulator Substrates

2009 ◽  
Vol 1185 ◽  
Author(s):  
Vincent Paillard ◽  
Jesse Groenen ◽  
Pascal Puech ◽  
Younes Lamrani ◽  
Marek Kostrzewa ◽  
...  
Keyword(s):  
Silicon Nitride ◽  
Compressive Strain ◽  
Uniaxial Stress ◽  
Nitride Layer ◽  
Silicon On Insulator ◽  
Strained Silicon ◽  
Silicon Nitride Layer ◽  
Uv Raman Spectroscopy ◽  
Uv Raman ◽  
Theoretical Results

AbstractCompressive strained Silicon from a Silicon on Insulator (SOI) substrate is obtained by replacing the buried oxide layer by a strained silicon nitride layer. The silicon overlayer and the buried dielectric are etched down to the substrate to form narrow wires (down to 300 nm wide). The Si overlayer is then expected to acquire compressive strain thanks to the relaxation of the SiN layer. The goal is to obtain a high uniaxial stress perpendicular to the wires. The structures and the strain are modeled using finite element simulations. The strain elements are used to calculate Raman spectra. Theoretical results are compared to experimental profiles deduced from resonant (UV) micro Raman experiments.

scholarly journals Implementation and acceleration of optimal control for systems biology

2021 ◽  
Vol 18 (181) ◽  
pp. 20210241
Author(s):  
Jesse A. Sharp ◽  
Kevin Burrage ◽  
Matthew J. Simpson
Keyword(s):  
Optimal Control ◽  
Systems Biology ◽  
Iteration Process ◽  
System Size ◽  
Sweep Method ◽  
Acceleration Techniques ◽  
Fixed Point Iteration Process ◽  
Allocation Decisions ◽  
Insight Into ◽  
Forward Backward Sweep Method

Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021 .

Sign in / Sign up

Export Citation Format

Share Document