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## M Schwalm Publication

Area of interest: Condensed matter theory, specialized in computer modeling of physical

processes

**Ph. D. dissertation and related work** : photoelectron spectroscopy (theory)

### Vector difference calculus

"Vector difference calculus for physical lattice models", W. Schwalm, B. Moritz, M. Giona and M.Schwalm, Phys. Rev. E 59 1217-1233 (1999).

### Surfaces and interfaces

"Surface density of states for directional photoemission spectroscopy of W(001)", J. Hermanson,

M. Kawajiri, W. A. Schwalm, Sol. St. Commun. 21, 327 (1977).

"Surface density of states for normal photoemission from Mo(110) and W(111)", J. Hermanson,

M. Kawajiri, and W. A. Schwalm, Sol. St. Commun. 25, 303 (1978).

"Computation of surface states on BCC transition metals", M. Kawajiri, (Thesis, Montana State

University, University Microfilms, Xerox,1978).

"Quantum theory of the double layer: A model of the electrode-electrode interface", B. Johnson,

J. Woods Halley, D. Price and M. K. Schwalm, Phys. Rev. B 31, 7695-7709 (1985).

### Kubo-Greenwood conductance and Anderson localization

"Electronic properties of fractal glass models", W. A. Schwalm and M. K. Schwalm, Phys. Rev.

B 39, 12872-12882 (1989).

"Length scaling of corner-to-corner propagation on fractal lattices," W. A. Schwalm M. K. Schwalm

and K. Rada, Phys. Rev. B 44, 382-385 (1991).

"Perfect conductance on fractal lattices", W. A. Schwalm and M. K. Schwalm, pp. 349-357 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, 15086-15093 (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, 4717-4729 (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, 4731-4744 (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,

5065-5076 (1996).

"Renormalization Analysis 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. Giustiani,

Langmuir 13, 1128-1137 (1997).

"Analysis of linear transport phenomena on fractals" M. Giona, W. A. Schwalm, A. Adrover and

M. K. Schwalm, The Chemical Engineering Journal, 64, 45-61 (1996).

"First-order 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, 2273-2282 (1996).

"Renormalization analysis of diffusion and adsorption on fractal and disordered lattices in thepresence of energetic disorder", M. K. Schwalm, M. Giona, W. A. Schwalm, A. Adrover and M. Giustiniani, Langmuir, 13,1128-1137 (1997).

"Diffusion of material andenergy on Vicsek and related lattices", M. K. Schwalm, D. K. Ludlow

and H. Ni in Fractals and Chaos in Chemical Engineering, M. Giona and G. Biardi eds.

(World Scientific, 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).

"Solution of transport schemes on fractals by means of Green function renormalization--

Application to integral quantities", M. Giona, A. Adrover, W. A. Schwalm and M. K. Schwalm,

Fractals, 57 473-491 (1997).

### Infinitely ramified structures

"Extension theory for lattice Green functions", W. A. Schwalm and M. K. Schwalm, Phys. Rev.

B 37, 9524-9542 (1988).

"Effects of surface roughness on transport in quasi-one-dimensional and - two-dimensional ballistic

channels", M. K. Schwalm and W. A. Schwalm, Phys. Rev. B 45, 6868-6876 (1992).

"Damping effects on the Kubo-Greenwood conductance of various lattice models in one, two andthree dimensions", W. A. Schwalm and M. K. Schwalm, Phys. Rev. B 45, 1770-1775 (1992).

"Green function renormalization: review of some results", M. Giona, W. A. Schwalm, A. Adrover

and M. K. Schwalm (to appear in a thematic issue of Fractals, T. Vicsek ed.)

"Dynamics of Cremona Maps from Physical Model"s, W. Schwalm, B. Moritz and M. Schwalm, Int.

3 J. of Modern Physics B15, 3279-3286 (2001).

"Gauge Simplification of Hamiltonian with Off-diagonal ±1" , M. Schwalm and W. Schwalm, Int.

J. of Modern Physics B15, 3287-3291 (2001).

### Closed formulas for Green functions on various fractal lattices

"Closed formulae for Green functions on fractal lattices," W. A. Schwalm and M. K. Schwalm,

Physica A 185, 195-201 (1992).

"Explicit orbits for renormalization maps for Green functions on fractal lattices", W. A. Schwalm

and M. K. Schwalm, Phys. Rev. B 47, 7847-7858 (1993).

"Explicit Green functions for hierarchical lattices", W. A. Schwalm, C. C. Reese, M. K. Schwalm

and C. J. Wagner, Phys. Rev. B 49, 15650-15663 (1994).

### Lie groups and reduction of order of renormalization recursions

"Conic pencils and renormalization dynamics", W. A. Schwalm, C. C. Reese, M. K. Schwalm andC. J. Wagner, Phys. Lett. A 193 238-244 (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 6741-6752 (1997).

"Group theoretic reduction of linear transport models on regular fractal structures"A, W. A. Schwalm,

M. K. Schwalm and M. Giona, Fractals and Chaos in Chemical Engineering, M. Giona and

G. Biardi eds.( World Scientific, 1997).

### Mathematical methods

"Generating functions in physics", W. A. Schwalm and M. K. Schwalm, Am. J. Phys. 51, 230-236

(1983).

"Bridge between particle and fluid kinematics", W. A. Schwalm and M. K. Schwalm, Am. J. Phys.

53, 421-428 (1985).

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