# PUBLICATIONS

**BOOKS**

C.C. Mei and B. Vernescu,

**Homogenization Methods for Multiscale Mechanics**,

*World Scientific Publishing Co.*, 2010.

J. Carbonara and B. Vernescu (eds),

**Creating Tomorrow’s Mathematics Professionals**,

*CO**MAP*, 2013.

RESEARCH PAPERS

RESEARCH PAPERS

G. Panasenko, K. Pileckas and B. Vernescu Steady state non-Newtonian ow with shear rate

dependent viscosity in thin tube structure with no slip boundary condition, to be submitted.

G. Nika and B. Vernescu, Micro-geometry effects on the nonlinear effective yield strength response of magnetorheological fluids, submitted.

G. Nika and B. Vernescu, Homogenization for a multi-scale model of magnetorheological suspension, Z. Angew. Math. Phys. (2020) 71: 14. https://doi.org/10.1007/s00033-019-1238-4.

G. Panasenko and B. Vernescu, Non-Newtonian flows in domains with non-compact boundaries, Nonlinear Analysis, 183 (2019) pp. 214-229.

J. E. C. Lope, R. Sato and B. Vernescu, Well-posedness of steady state Navier-Stokes equations with slip boundary conditions, Applicable Analysis, 98, 1-2 (2019) pp. 295-309.

P. Donato, S. Mardare and B. Vernescu, Bingham flows in periodic domains of infinite length, Chin. Ann. Math. Ser. B, 39 (2), (2018) pp. 183-200.

S. Jimenez and B. Vernescu, Derivation of the Navier slip and slip length for viscous flows over a rough boundary, Physics of Fluids 29, 057103 (2017).

G. Nika and B. Vernescu, Rate of Convergence for a multiscale model of dilute emulsions with non-uniform surface tension, Discrete Cont. Dyn. Systems-S, 9, 5 (2016) pp. 1553-1564.

D. Giachetti, B. Vernescu and M. A. Vivaldi, Asymptotic analysis of singular problems in perforated cylinders, Differential and Integral Equations, 29, 5-6 (2016) pp. 531-562.

G. Nika and B. Vernescu, Dilute emulsions with surface tension, Quarterly for Applied Mathematics, LXXIV, 1 (2016) pp. 89-111.

S. Jimenez and B. Vernescu, Nonlinear Neutral Inclusions: Assemblages of Coated Ellipsoids, R. Soc. open sci 2015. 2: 140394.

G. Nika and B. Vernescu, Asymptotics for dilute emulsions with surface tension , Journal of Elliptic and Parabolic Equations, 1 (2015) pp. 215-230.

F. Maris, Y. Gorb and B. Vernescu, Homogenization for Rigid Suspensions with Random, Velocity-Dependent Interfacial Forces, J. Math. An. Appl., 420, 1 (2014) pp. 632-668.

F. Maris, B. Vernescu, Effective Slip for Stokes Flows Across Randomly Leaky Permeable Membranes, Asymptotic Analysis, 86, 1 (2014) pp. 17-48.

P. Donato, S. Mardare and B. Vernescu, Darcy Equations in an Infinite Strip: Do Limits Commute?, Differential and Integral Equations, 26, 9-10 (2013) pp. 949-974.

S. Jimenez, B. Vernescu and W. Sanguinet, Neutral inclusions: assemblages of spheres, *Int. J. Solids and Structures*, ** 40**, 14-15, (2013) pp. 2231-2238.

B. S. Tilley, B. Vernescu and J. Plummer, Geometry-Driven Charge Accumulation in Electrokinetic Flows between Thin, Closely Spaced Laminates , *SIAM J. Appl. Math.*, **72**, 1 (2012) pp. 39-60.

F. Maris, B. Vernescu, Effective leak conditions across a membrane, *Complex Variables and Elliptic Equations*, ** 57**, 2-4 (2012) 437-453.

D. Onofrei, B. Vernescu, Asymptotic analysis of second-order boundary layer correctors, *Applicable Analysis*, **91**, 6 (2012) 1097-1110.

B. S. Tilley, B. Vernescu and J. Plummer, Electrokinetically-driven flows in swelling porous media, *Proc. 16th National Congress of Theoretical and Applied Mechanics,* USNCTAM 2010, June 27-July 2, State College, PA.

D. Onofrei and B. Vernescu, Error Estimates for Periodic Homogenization with non- smooth coefficients, *Asymptotic Analysis*, **54**, (2007) 103-123.

D. Onofrei, B. Vernescu, G-convergence Results for some Spectral Problems Associated to the Neumann Sieve and their Applications, * Multi Scale Problems and Asymptotic Analysis*, eds. A. Damlamian et. al., GAKUTO International Series, Mathematical Sciences and Applications, **24**, (2005) 249-260.

I. Ionescu, D. Onofrei, B. Vernescu, Gamma-Convergence for a Fault Model with Slip-Weakening Friction and Periodic Barriers, * Quarterly for Applied Mathematics*, LXIII, **4**, (2005) 747-778.

D. Onofrei, B. Vernescu, Asymptotics of a Spectral Problem Associated to the Neumann Sieve, * Analysis and Applications*, **3**, 1, (2005), 69-87.

B. Vernescu, Multiple-scale Analysis of Electrorheological Fluids, * International Journal of Modern Physics B*, **16**, 17-18, (2002), 2643-2648.

B. Vernescu, Multiple-scale Analysis of Electrorheological Fluids, * Electrorheological Fluids and Magnetorheological Suspensions*, ed. G. Bossis, Proceedings of the 8th International Conference, Nice, France, 9-13 July, 2001, World Scientific, 2002, 733-738.

J. Perlak and B. Vernescu, The Effective Yield Stress in Electrorheological Fluids, * Rev. Roum. Math. Pures et Appl.*, **45**, 2, (2000), 287-299.

R. Lipton and B. Vernescu, Bounds for Cell Wall Permeabilities, * IUTAM Symposium on Synthesis in Bio Solid Mechanics*, eds. P. Pedersen and M. P. Bendsoe, Kluver Academic Publishers, (1999), 401-406.

B. Vernescu, Size and Double-Layer Effects on the Macroscopic Behavior of Clays * Recent Advances in Problems of Flow and Transport in Porous Media*, eds. J. M. Crolet and M. E. Hatri, Kluver, (1998) 45-58.

D. Apelian, J. L. Hoffman, B. Vernescu, Deep Bed Filtration of Molten Metals, * Proc. International Conference and its Application in Science, Engineering and Industry,*

H. I. Ene and B. Vernescu, On the Macroscopic Behaviour of Clays, * Mathematical Modelling of Flow through Porous Media*, eds. Bourgeat, Carrasso, Luckhaus, Mikelic, World Scientific, (1995), 138-147.

R. Lipton and B. Vernescu, Variational Methods, Size Effects and Extremal Microgeometries for Elastic Composites with Imperfect Interface, * Mathematical Models and Methods in Appl. Sci.*, **5**, (1995), 1139-1173,

R. Lipton and B. Vernescu, Critical Radius, Size Effects and Extremal Microgeometries for Composites with Imperfect Interface, * J. Appl. Physics*, **9**, (1996), 8964-8969

R. Lipton and B. Vernescu, Two-phase Elastic Composites with Interfacial Slip, * Zeitschrift fur Angewandte Mathematik und Mechanik, (ZAMM)*, **76**, 2, (1996), 597

R. Lipton and B. Vernescu, Composites with Imperfect Interface, * Royal Society of London Proceedings*, **452**, (1996), 329-358.

H. I. Ene and B. Vernescu, Viscosity Dependent Behaviour of Viscoelastic Porous Media, * Asymptotic Theories for Plates and Shells*, eds. R. P. Gilbert and K. Hackl, Pitman Research Notes in Mathematics 319, (1995).

R. Lipton and B. Vernescu, Homogenization of Two-Phase Emulsions, * Proceedings of the Royal Society of Edinburgh*, **124A**, (1994) 1119-1134.

B. Vernescu, Asymptotic Analysis for an Incompressible Fluid Flow in Fractured Porous Media, * Int. J. Engng. Sci. 28*, **9**, (1990), 959-964.

B. Vernescu, Viscoelastic behaviour of a Porous Medium With a Deformable Skeleton, * St. Cerc. Mat. 4*, **5**, (1989), 423-440.

R. Stavre and B. Vernescu, Free Boundary Properties in non-Homogeneous Media Fluid Flow, * Int. J. Engng. Sci. 27*, **4**, (1989), 399-409.

I. R. Ionescu and B. Vernescu, A Numerical Method for a Viscoplastic Problem. An Application to Wire Drawing, * Int. J. Engng. Sci. 26*, **6**, (1988), 627-633.

R. Stavre and B. Vernescu, The Free Boundary Problem for the Anisotropic Dam, * Arch. Mech.*, **40**, (1988), 455-463.

R. Stavre and B. Vernescu, A Free Boundary Problem in Fluid Mechanics, * Proc. Conf. Diff. Eqs.} Cluj-Napoca, (1985).*

I. R. Ionescu, I. Molnar, and B. Vernescu, A Finite Element Model of Wire Drawing. Variational Formulation and Numerical Method Rev. Roum. Sci. Tech. Mech. Appl. 30, **6**, (1985), 611-622.

H. I. Ene and B. Vernescu, Homogenization of a Singular Perturbation Problem, Rev. Roum. Math.Pures et Appl., ** 30**, 10, (1985), 815-822.

R. Stavre and B. Vernescu, Incompressible Fluid Flow through a non-Homogeneous and Anisotropic Dam, Nonlinear Analysis TMA 9, **8**, (1985), 799-810.

B. Vernescu, On the Convergence of Functionals` Minimum Points, Rev. Roum. Math.Pures et Appl., **30**, 8, (1985), 685-692.

**MATHEMATICS EDUCATION**

J. Carbonara, B. Vernescu, Science Master’s Programs in Mathematical Sciences, Creating Tomorrowâ€™s Mathematics Professionals, J. Carbonara and B. Vernescu (eds.), NPSMA Workshop, Niagara Falls, NY, October 11-13, 2011, pp vii-xv, 2013.

B. Vernescu, The Vertical Integration of Industrial Mathematics – the WPI experience, Educational Interfaces between Mathematics and Industry, A. Damlamian et. al. (eds.), ICMI Study Series, Springer, vol 16, pp 253-260, 2013.

B. Vernescu, The Vertical Integration of Industrial Mathematics- the WPI experience, Proceedings EIMI 2010, Lisbon, Portugal, April 19-23, A. Araujo, A. Fernandez, A, Azevedo and J. F. Rodrigues (eds).

D. Berkey and B. Vernescu, A Model for Vertical Integration of Real-World Problems in Mathematics, *Proceedings of the 2007 ASEE Annual Conference*, 2007.

A. C. Heinricher and B. Vernescu, How Can Mathematics Help – Mathematicians at Work Today, *Pithagorean Review, Mu Alpha Theta on-line Journal*, 2002.

B. Vernescu and A. C. Heinricher, Research Experience for Undergraduates in Industrial Mathematics and Statistics at WPI, *Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs*, AMS, Providence, Rhode Island, 2000, J. A. Gallian ed.