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Porous Invariants [chapter]

Engel Lefaucheux, Joël Ouaknine, David Purser, James Worrell
2021 Lecture Notes in Computer Science  
AbstractWe introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely  ...  Nevertheless, we show that in many cases such invariants can be automatically synthesised, and moreover can be used to settle (non-)reachability questions for various interesting classes of affine loops  ...  R Invariants: R-linear and R-semi-linear Before delving into porous invariants, let us consider invariants over the real numbers, i.e., described as R-(semi)-linear sets.  ... 
doi:10.1007/978-3-030-81688-9_8 fatcat:5dx3ny3iazdilav2ql7avf2la4

Porous Invariants [article]

Engel Lefaucheux, Joël Ouaknine, David Purser, James Worrell
2021 arXiv   pre-print
We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely  ...  Nevertheless, we show that in many cases such invariants can be automatically synthesised, and moreover can be used to settle (non-)reachability questions for various interesting classes of affine loops  ...  The POROUS Tool Our invariant-synthesis tool porous 11 computes N-semi-linear invariants for point and Z-linear targets on systems defined by one-dimensional affine functions. porous includes implementations  ... 
arXiv:2106.00662v1 fatcat:snblqlbzbfbx7cuvg7cs27rcby

Cardinal invariants of strongly porous sets

Osvaldo Guzmán, Michael Hrušák, Arturo Martinez-Celis
2017 Journal of Logic and Analysis  
In this work we study cardinal invariants of the ideal SP of strongly porous sets on ω 2.  ...  We also find a connection between strongly porous sets on ω 2 and the Martin number for σ -linked partial orders, and we use this connection to construct a model where all the Martin numbers for σ -k-linked  ...  Journal of Logic & Analysis 9:6 (2017) Cardinal Invariants of Strongly Porous Sets Journal of Logic & Analysis 9:6 (2017) Journal of Logic & Analysis 9:6 (2017) Cardinal Invariants of Strongly  ... 
doi:10.4115/jla.2017.9.6 fatcat:32uqb4yhjbgiplactdl4fufg2m

Invariant manifolds for the porous medium equation [article]

Christian Seis
2015 arXiv   pre-print
We show how these invariant manifolds can be used to extract information on the higher-order long-time asymptotic expansions of solutions to the porous medium equation.  ...  In this paper, we investigate the speed of convergence and higher-order asymptotics of solutions to the porous medium equation posed in R^N.  ...  On the level of the porous medium equation (1.1), this corresponds to the invariance of solutions under the rescaling of mass.  ... 
arXiv:1505.06657v1 fatcat:sp2ajikgu5gynfvr36jhnxuuky

Cardinal invariants of monotone and porous sets

Michael Hrušák, Ondřej Zindulka
2012 Journal of Symbolic Logic (JSL)  
Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants of these ideals are also investigated.  ...  We investigate cardinal invariants of theσ-idealMongenerated by monotone subsets of the plane.  ...  Michael Hrušák (joint work with Ondřej Zindulka)Cardinal invariants of monotone and porous sets  ... 
doi:10.2178/jsl/1327068697 fatcat:f7ni7mkbw5glrk2a3pgtq3cvxm

The optimal system, similarity reduction and group-invariant solutions to the Fractional Porous Medium equation and Fractional Dual Porous Medium equation [article]

Ying Yang, Li-zhen Wang
2019 arXiv   pre-print
In this paper, we developed the group analysis to the time Fractional Porous Medium Equation (FPME) and the time Fractional Dual Porous Medium Equation (FDPME).  ...  Based on the above results, similarity reductions are performed and some explicit group invariant solutions are constructed.  ...  And the Dual Porous medium equation has been discussed in [11] with the invariant subspace method.  ... 
arXiv:1901.03666v1 fatcat:b6ufzpzyzzhmnohqdqsxnd2zby

CONCENTRATION OF INVARIANT MEASURES FOR STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS

MICHAEL RÖCKNER, FENG-YU WANG
2007 Infinite Dimensional Analysis Quantum Probability and Related Topics  
By using Bernstein functions, existence and concentration properties are studied for invariant measures of the infinitesimal generators associated to a large class of stochastic generalized porous media  ...  Analogous results are also proved for invariant probability measures for strong solutions.  ...  The main purpose of this paper is to study the invariant measures, in particular, their support (concentration) properties, associated to the following stochastic generalized porous medium equation (see  ... 
doi:10.1142/s0219025707002798 fatcat:wmgnyq4myfhkfonfnwf2g2zox4

Consequences of the Translation Invariance on the Darcy Free Convection Flow Past a Vertical Surface

Eugen Magyari
2010 Transport in Porous Media  
It is shown that the governing equation for the stream function of the Darcy free convection boundary layer flows past a vertical surface is invariant under arbitrary translations of the transverse coordinate  ...  On this reason it is invariant under any uniform translation Y → Y + Y 0 of this coordinate.  ...  In this large class of heat and fluid flow phenomena, the free convection past hot vertical surfaces embedded in saturated porous media has especially been promoted by important applications in geothermal  ... 
doi:10.1007/s11242-010-9590-z fatcat:5zb3pkkmh5c6xe5melwzyguvca

Group Invariant Solutions for Flow and Heat Transfer of Power-Law Nanofluid in a Porous Medium

Saba Javaid, Asim Aziz, A. M. Bastos Pereira
2021 Mathematical Problems in Engineering  
The flow is caused by the impulsive movement of the plate embedded in Darcy's type porous medium.  ...  The present work covers the flow and heat transfer model for the power-law nanofluid in the presence of a porous medium over the penetrable plate.  ...  plate within the porous medium.  ... 
doi:10.1155/2021/9942425 fatcat:3a7ujwumjjdmhhxp3fgjk5j4qi

Modeling Flow and Pressure Fields in Porous Media with High Conductivity Flow Channels and Smart Placement of Branch Cuts for Variant and Invariant Complex Potentials

Khanal, Weijermars
2019 Fluids  
Examples of such branch cut choices are given for so-called areal doublets and areal dipoles, which are powerful tools to describe the streamlines and pressure fields for flow in porous media with enhanced  ...  A long overdue distinction between so-called variant and invariant complex potentials is proposed here for the first time.  ...  , and 20) show that the presence of such flow channels have a significant impact on the flow in porous media.  ... 
doi:10.3390/fluids4030154 fatcat:rbidkwnysrcyddzygky3i7f6zi

Invariant Solutions for the Unsteady Magnetohydrodynamics (MHD) Flow of a Fourth-Grade Fluid Induced Due to the Impulsive Motion of a Flat Porous Plate

Taha Aziz, A. B. Magan, F. M. Mahomed
2014 Brazilian journal of physics  
The flow is caused by the motion of the porous plate in its own plane with an impulsive velocity V (t).  ...  An analysis is carried out to study the timedependent flow of an incompressible electrically conducting fourth-grade fluid over an infinite porous plate.  ...  At y = 0, the fluid is bounded by an infinite porous plate.  ... 
doi:10.1007/s13538-014-0292-9 fatcat:waljuyksjbh2nmnv356kx4t5ly

Invariant Measures for a Stochastic Porous Medium Equation

Giuseppe Da Prato, Michael Röckner
Stochastic Analysis and Related Topics in Kyoto: In honour of Kiyosi Itô   unpublished
Introduction The porous medium equation ∂X ∂t = ∆(X m ), m ∈ N, (1.1) on a bounded open set D ⊂ R d has been studied extensively.  ...  Our approach to this is first to look for an invariant measure for the solution to equation (1.2) which can now be defined "infinitesimally"(cf.  ... 
doi:10.2969/aspm/04110013 fatcat:h44cgdymfnferbdfznaiv4s6ji

Invariance analysis and similarity solution of heat transfer for MHD viscous power-law fluid over a non-linear porous surface via group theory

R Darji, M Timol
2013 International Journal of Advances in Applied Mathematics and Mechanics   unpublished
Mathematical formulation Consider a two-dimensional flow of an incompressible viscous fluid past a porous non-linear surface (stretching/shrinking sheet) at 0 y = .  ...  Now we have proceeded in our analysis to obtain a complete set of absolute invariants.  ... 
fatcat:luu3ko7v7jfzhavisqju3sgaqq

New analytic criterion for porous solids with pressure-insensitive matrix [article]

Oana Cazacu, Benoit Revil-Baudard
2016 arXiv   pre-print
In this paper, we address the question of how the relative weighting of the two invariants of the plastic deformation of the matrix influence the mechanical response of a porous metallic material.  ...  The relative weight of the two invariants is described by a material parameter b.  ...  Role played by the matrix sensitivity to the third-invariant on the mechanical response of the porous solid 4.1.  ... 
arXiv:1605.06717v1 fatcat:pvvg7sbkhbdyfilgcd2jhfycum

On Modeling Plasticity-damage Couplings in Polycrystalline Materials

Benoit Revil-Baudard, Oana Cazacu
2014 Procedia Materials Science  
At present, modeling of the plastic response of porous solids is done using stress-based plastic potentials.  ...  In this paper, for the first time strain rate-based potentials for porous solids with Tresca and von Mises matrices are obtained.  ...  The exact SRP for a porous von Mises solid and for a porous Tresca solid (Eq. (8)) are centro-symmetric i.e. they are invariant to the transformation (D m , R, ) → (-D m , R,-).  ... 
doi:10.1016/j.mspro.2014.06.230 fatcat:k6q6dzksk5dexhwode5eq7qqwy
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