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Applications of Symmetry Methods to Partial Differential Equations (2010)by G. Bluman, A. F. Cheviakov, and S. C. Anco,

Springer: Applied Mathematical Sciences, Vol. 168,

ISBN 978-0-387-98612-8.

- A.C., V. A. Dorodnitsyn, E. I. Kaptsov. Invariant Conservation Law-Preserving Discretizations of Linear and Nonlinear Wave Equations. Journal of Mathematical Physics 61.8 (2020): 081504. [PDF]
- S. Anco and A.C. "On the different types of global and local
conservation laws for partial differential equations in three spatial
dimensions: review and recent developments."
*International Journal of Non-Linear Mechanics*(2020): 103569. [PDF] - Dierkes, Dominik, A.C., and Martin Oberlack. New similarity reductions and exact solutions for helically symmetric viscous flows. Physics of Fluids 32.5 (2020): 053604. [PDF]
- Popovych, Roman O. A.C. Variational symmetries and conservation laws of the wave equation in one space dimension. Applied Mathematics Letters 104 (2020): 106225. [PDF]
- Ridgway, Wesley and A.C. Locally and globally optimal configurations of N particles on the sphere with applications in the narrow escape and narrow capture problems." Physical Review E 100.4 (2019): 042413. [PDF]
- Thiessen, Ryan and A.C. Nonlinear dynamics of a viscous bubbly fluid. Communications in Nonlinear Science and Numerical Simulation 73 (2019): 244-264. [PDF]
- Gilbert, Jason and A.C. Globally optimal volume-trap arrangements for the narrow-capture problem inside a unit sphere. Physical Review E 99.1 (2019): 012109. [PDF]
- Ridgway, Wesley and A.C. An iterative procedure for finding locally and globally optimal arrangements of particles on the unit sphere. Computer Physics Communications 233 (2018): 84-109. [PDF]
- A.C. Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model. Physica D: Nonlinear Phenomena 370 (2018): 14-28. [PDF]
- J. Heß and A. C. A solution set-based entropy principle for constitutive modeling in mechanics. Continuum Mechanics and Thermodynamics 31.3 (2019): 775-806. [PDF]
- A. C. and J. Heß. A symbolic computation framework for constitutive modelling based on entropy principles, Applied Mathematics and Computation 324 (2018) 105-118. [PDF]
- A. C. Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models, Computer Physics Communications 220 (2017) 56-73 [PDF]
- R. Naz and A. C. Conservation Laws and Nonlocally Related Systems
of Two-Dimensional Boundary Layer Models.
*Zeitschrift für Naturforschung A*72, no. 11 (2017): 1031-1051 [PDF] - A. C. and R. Naz. A recursion formula for the construction of local conservation laws of differential equations, J. Math.Anal.Appl. 448 (2017) 198–212 [PDF]
- A. C. and J.-F. Ganghoffer. One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes. Journal of the Mechanical Behavior of Biomedical Materials 58 (2016) 105-121 [PDF]
- A. C. and S. St. Jean. A comparison of conservation law construction approaches for the twodimensional incompressible Mooney-Rivlin hyperelasticity model. J. Math. Phys. 56, 121505 (2015) [PDF]
- A. Nold, M. Oberlack and A. F. Cheviakov. On new stability modes of plane canonical shear flows using symmetry classification. J. Math. Phys. 56, 113101 (2015) [PDF]
- A. C., J.-F. Ganghoffer, and S. St.Jean. Fully non-linear wave models in fiber-reinforced anisotropic incompressible hyperelastic solids. International Journal of Non-Linear Mechanics 71 (2015) 8–21 [PDF]
- A. C. and D. Gomez. Asymptotic analysis of narrow escape problems in nonspherical three-dimensional domains. Physical Review E 91, 012137 (2015) [PDF]
- A. C. and M. Oberlack. Generalized Ertel's theorem and infinite hierarchies of conserved quantities for three-dimensional time-dependent Euler and Navier Stokes equations. J. Fluid Mech. 760 (2014), 368-386 [PDF]
- Z. Yang and A. C., Some relations between symmetries of nonlocally related systems. J. Math. Phys. 55, 083514 (2014) [PDF]
- A. C., Conservation properties and potential systems of vorticity-type equations. J. Math. Phys. 55, 033508 (2014) [PDF]
- A. C., Symbolic Computation of Nonlocal Symmetries and Nonlocal Conservation Laws of Partial Differential Equations Using the GeM Package for Maple, Similarity and Symmetry Methods, Lecture Notes 165 in Applied and Computational Mechanics 73, Springer, 2014. [PDF]
- A. C., J.-F. Ganghoffer, and R. Rahouadj. Finite strain plasticity models revealed by symmetries and integrating factors: The case of Dafalias spin model. Int. J. of Plasticity 44 (2013), 47–67 [PDF]
- O. Kelbin, A. C., and M. Oberlack. New conservation laws of helically symmetric, plane and rotationally symmetric viscous and inviscid flows. J. Fluid Mech. 721 (2013), 340-366 [PDF]
- A. C. and D. Zawada. Narrow-escape problem for the unit sphere: Homogenization limit, optimal arrangements of large numbers of traps, and the N^2 conjecture. Phys. Rev. E 87 (2013), 042118 [PDF]
- C. Kallendorf, A. F. C, M. Oberlack, and Y. Wang, Conservation laws of surfactant transport equations. Physics of Fluids 24 (2012), 102105 [PDF]
- A. F. C, J.-F. Ganghoffer, Symmetry properties of two-dimensional Ciarlet–Mooney–Rivlin constitutive models in nonlinear elastodynamics. J. Math. Anal. Appl. 396 (2012), 625–639 [PDF]
- A.S. Reimer, A. C., A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet–Neumann boundary conditions. Computer Physics Communications 184 (2012), 783–798 [PDF]
- A. C., A.S. Reimer, M. J. Ward, Mathematical Modeling and Numerical Computation of Narrow Escape Problems. Phys. Rev. E 85 (2012), 021131 [PDF]
- A. C., Symbolic Computation of Local Symmetries of Nonlinear and Linear Partial and Ordinary Differential Equations. Math.Comput.Sci. 4 (2010), 203–222 [PDF]
- A. C. and G. W. Bluman, Multi-dimensional PDE Systems: Generating New Systems Via Conservation Laws, Potentials, Gauges, Subsystems. J. Math. Phys. 51 (2010), 103521 [PDF]
- A. C. and G. W. Bluman, Multi-dimensional PDE Systems: Nonlocal Symmetries, Nonlocal Conservation Laws, Exact Solutions. J. Math. Phys. 51 (2010), 103522 [PDF]
- A. C. and G. W. Bluman, On locally and nonlocally related potential systems. J. Math. Phys. 51 (2010), 073502 [PDF]
- A. C., M. J. Ward, and R. Straube, An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems: Part II: The Sphere. SIAM Multiscale Modeling and Simulation (2010) [PDF]
- A. C. and M. J. Ward, Optimizing the Principal Eigenvalue of the Laplacian in a Sphere with Interior Traps. Mathematical and Computer Modelling (2010) [PDF]
- A. C., Computation of fluxes of conservation laws, J. Eng. Math. 66 (2010), 153–173 [PDF]
- M. Oberlack and A. C., Higher-order symmetries and conservation laws of the G-equation for premixed combustion and resulting numerical schemes, J. Eng. Math. 66 (2010), 121–140 [PDF]
- G. W. Bluman, A. C., and J.-F. Ganghoffer, On the nonlocal symmetries, group invariant solutions and conservation laws of the equations of nonlinear dynamical compressible elasticity, Proc. IUTAM (2009) [PDF]
- A. C. and J. Hartwick, Constant Per Capita Consumption Paths with Exhaustible Resources and Decaying Produced Capital, Ecological Economics 68 (2009), 2969–2973 [PDF]
- G. W. Bluman, A. C., and S. C. Anco, Construction of
Conservation Laws: How the Direct Method Generalizes
Noether's Theorem, Proc. 4th Workshop ``Group Analysis of Differential
Equations &

Integrability'' (2009), 1-23. [PDF] - A. C., An extended procedure for finding exact solutions of partial differential equations arising from potential symmetries. Applications to gas dynamics, J. Math. Phys. 49 (2008), 083502 [PDF]
- G. Bluman, A. C., and J.-F. Ganghoffer, Nonlocally related PDE systems for one-dimensional nonlinear elastodynamics, J. Eng. Math. 62 (2008), 203–221 [PDF]
- G. Bluman, A. C., and M. Senthilvelan, Solution and Asymptotic/Blow-up Behaviour of a Class of Nonlinear Dissipative Systems, J. Math. An. Appl. 339 (2008), 1199-1209 [PDF]
- A. C. and S. C. Anco, Analytical properties and exact solutions of static plasma equilibrium systems in three dimensions, Phys. Lett. A 372 (2008), 1363-1373 [PDF]
- A. C. and M. J. Ward, A Two--Dimensional Metastable Flame-Front and a Degenerate Spike--Layer Problem, Interfaces and Free Boundaries 9 (2007), 513-547 [PDF]
- G. Bluman and A. C., Nonlocally related systems, linearization and nonlocal symmetries for the nonlinear wave equation, J. Math. An. Appl. 333 (2007), 93-111 [PDF]
- A. C., “GeM software package for computation of symmetries and conservation laws of differential equations”. Comp. Phys. Comm. 176 (2007), 48-61 [PDF]
- G. Bluman , A. C., and N. M. Ivanona, “Framework for nonlocally related PDE systems: simplification; new symmetries and conservation laws for NLT equations,” J. Math. Phys. 47 (2006), 113505 [PDF]
- G. Bluman and A. C. “Framework for potential systems and nonlocal symmetries: Algorithmic approach,” J. Math. Phys. 46 (2005), 123506 [PDF]
- A. C. “Construction of exact plasma equilibrium solutions with different geometries,” Phys. Rev. Lett. 94 (2005), 165001 [PDF]
- A. C. and J. Hartwick "Beckmann's Edgeworth-Bertrand Duopoly Example Revisited." Int. Game Theory Rev. 7 (4) (2005), 461-471.
- A. C. “Analytical 3-Dimensional Anisotropic Magnetohydrodynamic Equilibria.” Topology and its Applications 152 (2005), 157–173.
- A. C. “Exact plasma equilibria from symmetries and transformations of MHD and CGL equilibrium equations,” in: “Symmetry Methods in Physics” (ed. C.Burdik, O.Navratil, S.Posta), Prague, Czech Rep., ISBN 5-9530-0069-3 (2004) [PDF]
- A. C. and O. I. Bogoyavlenskij “Exact anisotropic MHD equilibria”, J. Phys. A 37 (2004), 7593-7607 [PDF]
- A. C. “Bogoyavlenskij symmetries of ideal MHD equilibria as Lie point transformations,” Phys. Lett. A 321 (2004), 34-49 [PDF]
- A. C. “Bogoyavlenskij symmetries of isotropic and anisotropic MHD equilibria are Lie point transformations”, Proc. Inst. Math. NAS Ukraine, 50 (2004), 69-76 [PDF]
- N. A. Kudryashov, G. S. Romanov, and A. C., “Numerical simulation of the quasistationary phase of a volcanic eruption in the initial stage”, Engineering-Physics Journal (Russian) / JEPTER (English) 76 (2003), 795-803 [PDF]
- N. A. Kudryashov, G. S. Romanov and A. C. “Numerical modeling of explosive volcanic eruptions”, Eng.-Phys. J. (Rus) / JEPTER (Eng). 75 (2002), 521-528.
- N. A. Kudryashov and A. C. “Self-Similar Solutions of 1-Dimentional Problems of Gas Filtration with Square Law of Resistance,” Eng.-Phys. J. (Rus) / JEPTER (Eng). 72 (1999), 1090-1099.

- "Conservation laws, similarity reductions and exact solutions for helically symmetric incompressible fluid flows," online Applied Mathematics Seminar, U. of Washington, USA, 14 May 2020 [PDF]
- "Symbolic Computation of Symmetries and First Integrals in Dynamical Systems," Winter CMS Meeting, December 8, 2019, Toronto, Canada [PDF]
- "Conservation laws, similarity reductions and exact solutions for helically symmetric incompressible fluid flows," Colloquium, Fudan University, June 2019 [PDF]
- "Conservation laws of partial differential equations: theory, computation, and examples" Departmental seminar, Mathematics and Statistics, U. Calgary, June 9, 2019 [PDF]
- "Narrow Escape and Narrow Capture problems in 3D, asymptotic solutions, optimal trap configurations", IMACS Nonlinear Waves, Athens, GA, USA, April 18, 2019 [PDF]
- "Exact Solutions of a Fully Nonlinear Two-Fluid Model", Keldysh Inst. for Applied Math., Moscow, Russia, June 28, 2018 [PDF]
- "The Narrow Escape Problem for the Unit Sphere and Other 3D Domains: Asymptotic Solution, Homogenization Limit, and Optimal Trap Arrangements", Conference "Problems of Mathematical Physics and Mathematical Modelling", MEPhI, Moscow, Russia, June 26, 2018 [PDF]
- "Global and Local Conservation Laws for Physical Models: Theory, Computation and Examples", Moscow State Engineering-Physics Inst., Moscow, Russia, June 21, 2018 [PDF]
- "Global and local conservation laws for physical models: Cases of static and moving domains." Seminar, TU Darmstadt, May 18, 2018 [PDF]
**Topical School on ‘Symmetry, similarity methods and conservation laws in solid and fluid mechanics’, Cargese, France, 2018**- A.C. Talk 1: Symmetries of Differential Equations: Symbolic Computation using Maple [PDF]
- A.C. Talk 2: On Symmetries of Linear and Nonlinear PDEs [PDF]
- A.C. Talk 3: Equivalence Transformations and Their Symbolic Computation [PDF]
- A.C. Talk 4: Symmetries of Di erential Equations: Practical session [PDF]

- "Conservation Laws of Differential Equations: Origins, Modern Approach, Properties, Systematic Computation, and Applications" McMaster University Colloquium, LAMA/CNRS (Chambery, France) talk, 10/2017 [PDF]
- "Conservation laws of partial differential equations: different types, physical meaning, systematic computation, properties, and examples." 3rd International Conference on Symmetry of Differential Equations and Applications (SDEAIII) İstanbul, Turkey, 08/2017 [PDF]
- "Local and Global Optimization of Particle Locations on the Sphere: Models, Applications, Mathematical Aspects, and Computations." SIAM DS17 meeting, Snowbird, Utah, 05/2017 [PDF]
- "A Recursion Formula for the Construction of Local Conservation Laws of Differential Equations", Canadian Mathematical Society (CMS) 2017 Winter meeting, Niagara Falls, Canada, 12/2016 [PDF]
- "Exact Solutions of a Fully Nonlinear Two-Fluid Model". Canadian Society of Applied and Industrial Mathematics (CAIMS) 2016 meeting, Edmonton, Canada, May 27, 2016 [PDF]
- "Conservation law construction for the incompressible Mooney-Rivlin hyperelasticity model." Canadian Mathematical Society (CMS) 2016 Summer meeting, Edmonton, Canada, May 26, 2016.
- "Conservation laws of vorticity-type equations", Canadian Mathematical Society (CMS) 2016 Summer meeting, Edmonton, Canada, May 25, 2016 [PDF]
- "Nonlinear Elastodynamic Models of Wave Propagation and Conservation Laws for Fiber-Reinforced Materials", Society for Industrial and Applied Mathematics (SIAM) Meeting 2016, Philadelphia, USA, May 11, 2016 [PDF]
- "The Fully Nonlinear Choi-Camassa Two-Fluid Model: Parameter Reduction and Exact Traveling Wave Solutions", Seminar - Strömungsdynamik, TU Darmstadt, Germany, April 4, 2016.
- "Local Conservation Laws for Nonlinear Differential Equations: Theory, Systematic Construction, Computation, and Examples", DIANA-Seminar, U. Vienna, 15 April 2016 [PDF]
- "Exact Solutions of a Fully Nonlinear Two-Fluid Model", Seminar, U. Vienna, 11 April 2016 [PDF]
- "The Fully Nonlinear Choi-Camassa Two-Fluid Model: Parameter Reduction and Exact Traveling Wave Solutions", Seminar, TU Darmstadt, Strömungsdynamik, April 2016 [PDF]
- "Conservation Laws of Fluid Dynamics Models", Seminar, Shanghai Maritime University, China, June 2015 [PDF]
- "Local Conservation Laws for Nonlinear Models: Theory, Systematic Construction, and Computation Examples", Seminar, Shanghai Maritime University and the University of Shanghai, China, June 2015 [PDF]
- "Asymptotic Analysis of Narrow Escape Problems in Non-Spherical 3D Domains" [Joint with D. Gomez], SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, May 2015 [PDF]
- "Conservation Laws of Models of Biological Membranes in the Framework of Nonlinear Elastodynamics" [Joint with J.-F. Ganghoffer], Euromech 560 Colloquium, Ascona, Switzerland, Feb. 2015 [PDF]
- "Conservation Laws for Nonlinear Equations: Theory, Computation, and Examples", LEMTA seminar, Univ. Lorraine, Nancy, France, Feb. 2015 [PDF]
- "Nonlinear Equations for Finite-Amplitude Wave Propagation in Fiber-Reinforced Hyperelastic Media", CMS winter meeting, Hamilton, Dec. 2014 [PDF]
- "Constitutive Relations, Natural States, and Traveling Waves in Two-Dimensional Nonlinear Elastodynamics", AMMP Seminar, University of Saskatchewan, September 2014 [PDF]
- "On Conservation Laws and Potential Systems of Vorticity-Type Equations", GADEIS VII, Cyprus, June 2014 [PDF]
- "Constitutive Relations, Natural States, and Traveling Waves in Two-Dimensional Nonlinear Elastodynamics", CMSC 2014, University of Saskatchewan, June 2014 [PDF]
- "The Narrow Escape Potential, Optimal Arrangements of N Traps on the Unit Sphere, and the Dilute Trap Limit for N>>1", Constructive Functions 2014, Vanderbilt University, Nashville, USA, May 2014 [PDF]
- "Nonlocally Related PDE Systems: History, Recent Developments, and Open Problems", Symmetry Conference in Honour of George Bluman, Vancouver, Canada, May 13-16, 2014 [PDF]
- "The Narrow Escape Problem for the Unit Sphere: Homogenization Limit, Optimal Trap Arrangements, and the N2 Conjecture", CMS Winter Meeting, December 2013 [PDF]
- "Conservation Laws For Viscous and Inviscid Flows in Helical, Plane and Rotational Symmetry", IMACS Nonlinear Waves Conference, UGA, Athens, GA, March 25, 2013 [PDF]
- "On Symmetry Properties of a Class of Constitutive Models in Two-Dimensional Nonlinear Elastodynamics", CMS winter meeting, Montreal, 2012 [PDF]
- "Systematic Construction of Conservation Laws of Nonlinear Partial Differential equations", Physics seminar, Bogazici University, Istanbul, Turkey, 2012 [PDF]
- "Mathematical Modeling and Numerical Computation of Narrow Escape Problems", INPL seminar, Nancy, France, 2012 [PDF]
- "Symmetry Methods for Differential Equations and Their Applications in Mathematical Modeling", Math Colloquium, University of Regina, Jan. 20, 2012 [PDF]
- "Conservation Laws of Surfactant Transport Equations", CMS Winter Meeting, Toronto, Dec. 2011 [PDF]
- "Conservation Laws: Systematic Construction, Noether's Theorem, Applications, and Symbolic Computations", Physics Seminar, UofS, Nov.10, 2011 [PDF]
- "A Maple-based Package for Computation of Conservation Laws, Symmetries and Invariant forms of DEs", ICIAM 2011, Vancouver [PDF]
- "Direct Method of Construction of Conservation Laws for Nonlinear Differential Equations, its Relation with Noether's Theorem, Applications, and Symbolic Software", INPL seminar, Nancy, France, 2011 [PDF]
- "Mathematical Modeling, Numerical Computation, and Applications of Narrow Escape Problems", PRNMS 2011, Regina [PDF]
**Session: "Symmetry Methods for Differential Equations", CMS-2010 winter meeting, Dec.3-5, 2010. Vancouver, BC, Canada**[**Talks**]- "An Asymptotic Analysis of the Mean First Passage Time for Narrow Escape Problems for the Sphere", Optimal Configurations on the Sphere and Other Manifolds, Vanderbilt University, 2010. [PDF]
- "Narrow Escape Problems: Asymptotic Optimization of Locations of Small Traps for the Unit Sphere", CMS-2009 winter meeting, [PDF]
- "An extended procedure for finding exact solutions of PDEs arising from potential symmetries", Symmetry in Nonlinear Mathematical Physics, Kiev, 2009 [PDF]
- "Computation and applications of local conservation laws", PNRMS, University of Saskatchewan, 2009 [PDF]
- "Nonlocally Related PDE Systems", TU Darmstadt, May 2008 [PDF]
- "Computation of Conservation Laws Admitted by PDEs", TU Darmstadt, May 2008 [PDF]
- "Computation of Point Symmetries Admitted by DEs", TU Darmstadt, May 2008 [PDF]
- "Modern Symmetry Methods for PDEs. Applications to Mathematical Modeling and Analysis". UofS, 2008. [PDF]

- "Exact Axially and Helically Symmetric Magnetohydrodynamic Equilibria" [PDF]

with**Jason Keller**(2019). - "Brownian Dynamics Modelling for the Narrow Escape Problem" [PDF]

with**Vaibhava Srivastava**,**Jason Gilbert**, and**Mohamad Alwan** - "Discrete Mathematical Modeling of Powder Bed 3D Printing Process" [PDF]

with**Travis Black**and**Chris Duffy**(2019). - "Narrow Capture Problems: Volume Traps in the Unit Sphere" [PDF]

with**Jason Gilbert,**summer undergraduate student (2017). - "Shear radial wave propagation models in ber-reinforced hyperelastic and
hyper-viscoelastic cylindrically symmetric media" [PDF]

with**Caylin Lee,**summer undergraduate student. - "Nonlinear Dynamics of Viscous Fluids with Gas Bubbles" [PDF]

with**Ryan J. Thiessen**, 2016 summer undergraduate student. - "Energy-Minimizing Arrangements of Repelling Particles on the Sphere:
Coulombic and Narrow Escape Potentials" [PDF]

with**Wesley J. Ridgway**, 2016 NSERC USRA summer undergraduate student. - "Shear Cylindrical Waves in the Framework of Finite
Fiber-Reinforced Hyper- and Viscoelasticity:
Applications to Blood Vessel Models" [PDF]

with**Caylin M. Lee**, 2016 NSERC USRA summer undergraduate student. - "Mathematical Modelling of the Dynamics of a
Viscous Fluid with Gas Bubbles" [PDF]

with**Jaden Dasiuk**, 2015 NSERC USRA summer undergraduate student. - "Study of Wave Propagation in Fiber-reinforced
Elastic Solids Using Lie Symmetry and Conservation
Law Analysis" [PDF]

with**Simon St. Jean,**M.Sc. student, presented at the CMSC-2014 conference, Saskatoon, Canada. - "Narrow Escape Problems in 3D Domains" (CMS Winter meeting,
December 2013) [PDF],

with**Daniel Gomez**, NSERC USRA / UofS USTEP summer undergraduate student. - "Narrow Escape Problems in Three-Dimensional Domains" (2013) [PDF],

with**Daniel Gomez**, NSERC USRA / UofS USTEP summer undergraduate student. - "Exact Solutions of Ideal Plasma Equilibria" (2011) [PDF],

with**Stephanie Goertzen**, UofS USTEP summer undergraduate student. - "Optimal
Arrangements and Homogenization Limit for Traps on the Sphere" (2011) [PDF],

with**Daniel Zawada**, NSERC USRA summer undergraduate student. - "Mathematical Modelling of Narrow Escape Problems"
(2010) [PDF],

with**Ashton Reimer**, NSERC USRA summer undergraduate student.

**"SYMMETRIES AND EXACT SOLUTIONS OF PLASMA EQUILIBRIUM EQUATIONS"**[PDF]

Queen's University at Kingston, 2004.

Supervisor: Prof. O. I. Bogoyavlenskij

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