List of Selected Publications
William A. Schwalm
Hierarchical analysis of nanostructured materials
and systems

Infinitely ramified structures

"Extension theory for lattice Green functions", W.
A. Schwalm and M. K. Schwalm, Phys. Rev. B 37, 95249542 (1988).

"Effects of surface roughness on transport in quasionedimensional
and  twodimensional ballistic channels", M. K. Schwalm and W. A. Schwalm,
Phys. Rev. B 45, 68686876 (1992).

"Damping effects on the KuboGreenwood conductance
of various lattice models in one, two and three dimensions", W. A. Schwalm
and M. K. Schwalm, Phys. Rev. B 45, 17701775 (1992).

"Solutions of transport schemes on fractals by means
of Green function renormalizationApplication to integral quantities",
M. Giona, A. Adrover, W. A. Schwalm and M. K. Schwalm, Fractals, 57
473491(1997).

KuboGreenwood conductance and Anderson localization

"Electronic properties of fractal glass models",
W. A. Schwalm and M. K. Schwalm, Phys. Rev. B 39, 1287212882 (1989).

"Length scaling of cornertocorner propagation on
fractal lattices," W. A. Schwalm M. K. Schwalm and K. Rada, Phys. Rev.
B 44, 382385 (1991).

"Perfect conductance on fractal lattices", W. A.
Schwalm and M. K. Schwalm, pp. 349357 in Fractals in the Natural and
Applied Sciences, M. M. Novak, editor (Elsevier, Amsterdam, 1994).

"Length scaling of conductance distribution for random
fractal lattices", M. K. Schwalm and W. A. Schwalm, Phys. Rev. B 54,
1508615093 (1996).

Application of formalism to chemical engineering

"Exact solution of linear transport equations in
fractal media I. Renormalization analysis and general theory" , M. Giona,
W. A. Schwalm, M. K. Schwalm and A. Adrover, Chem. Engng. Sci. 51,
47174729 (1996).

"Exact solution of linear transport equations in
fractal media II. Diffusion and Convection" M. Giona, W. A. Schwalm, M.
K. Schwalm and A. Adrover, Chem. Engng Sci. 51, 47314744 (1996).

"Exact solution of linear transport equations in
fractal media III. Adsorption and Chemical Reaction", M. Giona, A. Adrover,
W. A. Schwalm and M. K. Schwalm, Chem. Engng Sci. 51, 50655076
(1996).

"Analysis of linear transport phenomena on fractals"
M. Giona, W. A. Schwalm, A. Adrover and M. K. Schwalm, The Chemical Engineering
Journal 64, 4561 (1997).

"Firstorder kinetics in fractal catalysts: renormalization
analysis of the effectiveness factor", M. Giona, W. A. Schwalm, A. Adrover
and M. K. Schwalm, Chem. Engng Sci. 51, 22732282 (1996).

"Renormalization analysis of diffusion and adsorption
on fractal and disordered lattices in the presence of energetic disorder",
M. K. Schwalm, M. Giona, W. A. Schwalm, A. Adrover and M. Giustiniani,
Langmuir 13, 11281137 (1997).

"Scaling and scaling crossover for transport on anisotropic
fractal lattices", A. Adrover, W. A. Schwalm, M. Giona and D. Bachand,
Phys. Rev. E 55, 73047312 (1997).

"Perspectives and application of Green function renormalization
to transport phenomena", M. Giona, W. A. Schwalm, M. K. Schwalm and A.
Adrover in Fractals and Chaos in Chemical Engineering , M. Giona
and G. Biardi eds. (World Scientific, 1997).
Closed formulas for Green functions on fractal
lattices

"Closed formulae for Green functions on fractal lattices,"
W. A. Schwalm and M. K. Schwalm, Physica A 185, 195201 (1992).

"Explicit orbits for renormalization maps for Green
functions on fractal lattices", W. A. Schwalm and M. K. Schwalm, Phys.
Rev. B 47, 78477858 (1993).

"Explicit Green functions for hierarchical lattices",
W. A. Schwalm, C. C. Reese, M. K. Schwalm and C. J. Wagner, Phys. Rev.
B 49, 1565015663 (1994).
Lie groups and reduction of order of renormalization
recursions

"Conic pencils and renormalization dynamics", W.
A. Schwalm, C. C. Reese, M. K. Schwalm and C. J. Wagner, Phys. Lett. A
193 238244 (1994).

"Lie groups and solution of dynamical problems on
fractal lattices", W. A. Schwalm, M. K. Schwalm and M. Giona, in Fractal
Frontiers, M. M. Novak and T. G. Dewey eds. (World Scientific, 1997).

"Group theoretic reduction of Laplacian dynamical
problems on regular fractal structures", W. A. Schwalm, M. K. Schwalm and
M. Giona, Phys. Rev. E 55 67416752 (1997).

"Group theoretic reduction of linear transport models
on regular fractal structures", W. A. Schwalm, M. K. Schwalm and M. Giona
in Fractals and Chaos in Chemical Engineering, M. Giona and G. Biardi
eds.(World Scientific, 1997).

"Lie groups and discrete dynamical systems", B. Moritz,
W. Schwalm and D. Uherka (accepted, J. Phys. A, Mathematical and General)

"Finding Lie groups that reduce order of discrete
dynamical systems", B. Moritz, W. Schwalm and D. Uherka, J. Phys. A Math.
Gen. 31, 73797402 (1999).
Vector difference calculus for physical lattices

"Vector difference calculus for physical lattice
models", W. A. Schwalm, B. Moritz, M. Giona and M. K. Schwalm, Phys. Rev.
E 59, 12171233 (1999).

"Green function for coupled vector fields", B. Moriz and W. A. Schwalm, J. Phys A:Mth Gen.
34 589602(2001).
Stiff selfavoiding walks

"Biased interacting selfavoiding walks on the foursimplex
lattice", G. F. Tuthill and W. A. Schwalm, Phys. Rev. B 46, 1372213734
(1992).