Topological sectors, dimer correlations, and monomers from the transfer-matrix solution of the dimer model

The paper considers the steady-state harmonic response of an elastic fluid-loaded membrane supported by irregularly spaced ribs. Under the assumption of subsonic wave coupling, the solution is given exactly for any configuration as a product of 2 x 2 transfer matrices. It is well known that the response of a periodically ribbed membrane exhibits a pass/stop band structure. Although this structure is destroyed in the irregular case, we find that two distinct régimes remain: smooth and fluctuating exponential decay. The transfer matrix solution is used to explain these regions. The average transfer matrix is obtained exactly; where the decay is smooth its eigenvalues approximately determine the localization length.

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Transfer matrix solution of the Wako–Saitô–Muñoz–Eaton model augmented by arbitrary short range interactions

Journal of Statistical Mechanics Theory and Experiment ◽

10.1088/1742-5468/2010/08/p08028 ◽

2010 ◽

Vol 2010 (08) ◽

pp. P08028 ◽

Cited By ~ 1

Author(s):

V I Tokar ◽

H Dreyssé

Keyword(s):

Transfer Matrix ◽

Short Range ◽

Matrix Solution

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Analysis of skewed multibeam bridges by the transfer matrix method

Canadian Journal of Civil Engineering ◽

10.1139/l85-003 ◽

1985 ◽

Vol 12 (1) ◽

pp. 24-35

Author(s):

I. G. Buckle ◽

Weng-Onn Lee

Keyword(s):

Transfer Matrix ◽

Single Point ◽

Cross Coupling ◽

Highway Bridges ◽

Matrix Analysis ◽

Matrix Solution ◽

Transfer Matrix Analysis ◽

Support Conditions ◽

Skew Angles ◽

Span Width

The analysis of multibeam bridge decks is seriously complicated by the effect of skew. Conventional methods invoke grillage solutions, which have inherent difficulties. This paper proposes an extension of the transfer matrix solution for right decks to include the effects of skew without detracting from the simplicity of the method. Both the flexural and torsional flexibility coefficients need to be modified for the skew support conditions and a new flexure–torsion coefficient is introduced to represent the cross-coupling that occurs between these flexibilities because of skew. The assumption of load transference through a single-point hinge between adjacent beams is retained, but the spanwise location of this point is varied from beam to beam according to the degree of skew. Results are presented for a range of skew angles and span/width ratios and compared with those from a modified grillage solution; excellent agreement was demonstrated up to and including 45° skew. Key words: highway bridges, skew, transfer matrix analysis, grillage modelling, multibeam decks, single span, comparative solutions.

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