scholarly journals Conformal welding problem, flow line problem, and multiple Schramm–Loewner evolution

2020 ◽  
Vol 61 (8) ◽  
pp. 083301
Author(s):  
Makoto Katori ◽  
Shinji Koshida
Keyword(s):  
Flow Line ◽  
Conformal Welding ◽  
Loewner Evolution

scholarly journals UNIQUENESS OF THE WELDING PROBLEM FOR SLE AND LIOUVILLE QUANTUM GRAVITY

2019 ◽  
pp. 1-27 ◽  
Author(s):  
Oliver McEnteggart ◽  
Jason Miller ◽  
Wei Qian
Keyword(s):  
Quantum Gravity ◽  
Space Filling ◽  
Conformal Welding ◽  
Geometric Conditions ◽  
Simple Set ◽  
Welding Operation ◽  
Loewner Evolution ◽  
Quantum Disks

We give a simple set of geometric conditions on curves $\unicode[STIX]{x1D702}$ , $\widetilde{\unicode[STIX]{x1D702}}$ in $\mathbf{H}$ from $0$ to $\infty$ so that if $\unicode[STIX]{x1D711}:\mathbf{H}\rightarrow \mathbf{H}$ is a homeomorphism which is conformal off $\unicode[STIX]{x1D702}$ with $\unicode[STIX]{x1D711}(\unicode[STIX]{x1D702})=\widetilde{\unicode[STIX]{x1D702}}$ then $\unicode[STIX]{x1D711}$ is a conformal automorphism of $\mathbf{H}$ . Our motivation comes from the fact that it is possible to apply our result to random conformal welding problems related to the Schramm–Loewner evolution (SLE) and Liouville quantum gravity (LQG). In particular, we show that if $\unicode[STIX]{x1D702}$ is a non-space-filling $\text{SLE}_{\unicode[STIX]{x1D705}}$ curve in $\mathbf{H}$ from $0$ to $\infty$ , and $\unicode[STIX]{x1D711}$ is a homeomorphism which is conformal on $\mathbf{H}\setminus \unicode[STIX]{x1D702}$ , and $\unicode[STIX]{x1D711}(\unicode[STIX]{x1D702})$ , $\unicode[STIX]{x1D702}$ are equal in distribution, then $\unicode[STIX]{x1D711}$ is a conformal automorphism of $\mathbf{H}$ . Applying this result for $\unicode[STIX]{x1D705}=4$ establishes that the welding operation for critical ( $\unicode[STIX]{x1D6FE}=2$ ) LQG is well defined. Applying it for $\unicode[STIX]{x1D705}\in (4,8)$ gives a new proof that the welding of two independent $\unicode[STIX]{x1D705}/4$ -stable looptrees of quantum disks to produce an $\text{SLE}_{\unicode[STIX]{x1D705}}$ on top of an independent $4/\sqrt{\unicode[STIX]{x1D705}}$ -LQG surface is well defined.

THREE FLOW-LINE SYSTEMS WITH UNCERTAIN BAULKING

2009 ◽  
Vol 14 (02) ◽  
Author(s):  
D. de la Fuente ◽  
M.J. Pardo
Keyword(s):  
Flow Line

scholarly journals The Effect of Flow Lines on the Mechanical Properties in Hot-Rolled Bearing Steel

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 456
Author(s):  
Dongsheng Qian ◽  
Chengfei Ma ◽  
Feng Wang
Keyword(s):  
Mechanical Characterization ◽  
Tensile Deformation ◽  
Flow Line ◽  
Plastic Property ◽  
Bearing Steel ◽  
Mechanical Anisotropy ◽  
Flow Lines ◽  
Significant Difference ◽  
Hot Rolled ◽  
Bearing Rings

Hot rolling is an essential process for the shape-forming of bearing steel. It plays a significant role in the formation and distribution of flow lines. In this work, the effect of flow lines is investigated by analyzing the microstructure and mechanical anisotropy of hot-rolled bearing steel. It was found that carbides rich with Cr and Mn elements are distributed unevenly along the flow-line direction of the hot-rolled bearing steel. Moreover, the mechanical characterization indicates that ultimate tensile strength and yield strength do not have any significant difference in two directions. Nevertheless, an ultrahigh section shrinkage of 57.51% is obtained in the 0° sample that has parallel flow lines, while 90° sample shows poor section shrinkage. The uneven distributed carbides will affect the direction and speed of crack propagation during tensile deformation. Therefore, the 0° and 90° samples exhibit great difference in plastic property. Meanwhile, after tensile deformation, a delaminated texture is observed in the flow lines, which may be caused by different degrees of deformation of grains due to the uneven distribution of carbides. The results of this work may provide guidance for controlling and optimizing flow lines in the manufacturing of bearing rings.

scholarly journals Engineering Mathematical Analysis Method for Productivity Rate in Linear Arrangement Serial Structure Automated Flow Assembly Line

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Tan Chan Sin ◽  
Ryspek Usubamatov ◽  
M. A. Fairuz ◽  
Mohd Fidzwan B. Md. Amin Hamzas ◽  
Low Kin Wai
Keyword(s):  
Mathematical Model ◽  
Failure Rate ◽  
Mathematical Analysis ◽  
Assembly Line ◽  
Flow Line ◽  
Analysis Method ◽  
Machining Time ◽  
Linear Arrangement ◽  
Final Assembly ◽  
Productivity Rate

Productivity rate (Q) or production rate is one of the important indicator criteria for industrial engineer to improve the system and finish good output in production or assembly line. Mathematical and statistical analysis method is required to be applied for productivity rate in industry visual overviews of the failure factors and further improvement within the production line especially for automated flow line since it is complicated. Mathematical model of productivity rate in linear arrangement serial structure automated flow line with different failure rate and bottleneck machining time parameters becomes the basic model for this productivity analysis. This paper presents the engineering mathematical analysis method which is applied in an automotive company which possesses automated flow assembly line in final assembly line to produce motorcycle in Malaysia. DCAS engineering and mathematical analysis method that consists of four stages known as data collection, calculation and comparison, analysis, and sustainable improvement is used to analyze productivity in automated flow assembly line based on particular mathematical model. Variety of failure rate that causes loss of productivity and bottleneck machining time is shown specifically in mathematic figure and presents the sustainable solution for productivity improvement for this final assembly automated flow line.

scholarly journals The Age-Depth Profile in the Upper Part of a Steady-State Ice Sheet

1989 ◽  
Vol 35 (121) ◽  
pp. 406-417 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Flow Line ◽  
Numerical Models ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Western Slope ◽  
Simple Models

AbstractSimple analytical models are developed in order to study how up-stream variations in accumulation rate and ice thickness, and horizontal convergence/ divergence of the flow influence the age and annual layer-thickness profiles in a steady-state ice sheet. Generally, a decrease/increase of the accumulation rate and an increase/decrease of the ice thickness in the up-stream direction (i.e. opposite to the flow direction) results in older/younger ice at a given depth in the ice sheet than would result if the up-stream accumulation rate and ice thickness were constant along the flow line.Convergence/divergence of the up-stream flow will decrease/increase the effect of the accumulation-rate and ice-thickness gradients, whereas convergence/divergence has no influence at all on the age and layer-thickness profiles if the up-stream accumulation rate and ice thickness are constant along the flow line.A modified column-flow model, i.e. a model for which the strain-rate profile (or, equivalently, the horizontal velocity profile) is constant down to the depth corresponding to the Holocene/Wisconsinan transition 10 750 year BP., seems to work well for dating the ice back to 10 000–11 000 year B P. at sites in the slope regions of the Greenland ice sheet. For example, the model predicts the experimentally determined age profile at Dye 3 on the south Greenland ice sheet with a relative root-mean-square error of only 3% back to c. 10 700 year B.P. As illustrated by the Milcent location on the western slope of the central Greenland ice sheet, neglecting up-stream accumulation-rate and ice-thickness gradients, may lead to dating errors as large as 3000–000 years for c. 10 000 year old ice.However, even if these gradients are taken into account, the simple model fails to give acceptable ages for 10 000 year old ice at locations on slightly sloping ice ridges with strongly divergent flow, as for example the Camp Century location. The main reason for this failure is that the site of origin of the ice cannot be determined accurately enough by the simple models, if the flow is strongly divergent.With this exception, the simple models are well suited for dating the ice at locations where the available data or the required accuracy do not justify application of elaborate numerical models. The formulae derived for the age-depth profiles can easily be worked out on a pocket calculator, and in many cases will be a sensible alternative to using numerical flow models.

Effect of Grain Flow Orientation on Rolling Contact Fatigue Life of AISI M-50

1982 ◽  
Vol 104 (3) ◽  
pp. 330-334 ◽  
Author(s):  
A. H. Nahm
Keyword(s):  
Fatigue Life ◽  
Flow Line ◽  
Flow Direction ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
Vacuum Arc ◽  
Type I ◽  
Grain Flow ◽  
Contact Fatigue Life

Accelerated rolling contact fatigue tests were conducted to study the effect of grain flow orientation on the rolling contact fatigue life of vacuum induction melted and vacuum arc remelted (VIM-VAR) AISI M-50. Cylindrical test bars were prepared from a billet with 0, 45, and 90 deg orientations relative to billet forging flow direction. Tests were run at a Hertzian stress of 4,826 MPa with a rolling speed of 12,500 rpm at room temperature, and lubricated with Type I (MIL-L-7808G) oil. It was observed that rolling contact fatigue life increased when grain flow line direction became more parallel to the rolling contact surface.

Power matrices for Faber polynomials and conformal welding

2013 ◽  
Vol 58 (9) ◽  
pp. 1247-1259 ◽  
Author(s):  
Bryan Penfound ◽  
Eric Schippers
Keyword(s):  
Faber Polynomials ◽  
Conformal Welding
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