@article{13432,
  abstract     = {A new experimental technique is described that uses reaction−diffusion phenomena as a means of one-step microfabrication of complex, multilevel surface reliefs. Thin films of dry gelatin doped with potassium hexacyanoferrate are chemically micropatterned with a solution of silver nitrate delivered from an agarose stamp. Precipitation reaction between the two salts causes the surface to deform. The mechanism of surface deformation is shown to involve a sequence of reactions, diffusion, and gel swelling/contraction. This mechanism is established experimentally and provides a basis of a theoretical lattice-gas model that allows prediction surface topographies emerging from arbitrary geometries of the stamped features. The usefulness of the technique is demonstrated by using it to rapidly prepare two types of mold for passive microfluidic mixers.},
  author       = {Campbell, Christopher J. and Klajn, Rafal and Fialkowski, Marcin and Grzybowski, Bartosz A.},
  issn         = {1520-5827},
  journal      = {Langmuir},
  keywords     = {Electrochemistry, Spectroscopy, Surfaces and Interfaces, Condensed Matter Physics, General Materials Science},
  number       = {1},
  pages        = {418--423},
  publisher    = {American Chemical Society},
  title        = {{One-step multilevel microfabrication by reaction−diffusion}},
  doi          = {10.1021/la0487747},
  volume       = {21},
  year         = {2005},
}

@article{13435,
  abstract     = {Micropatterning of surfaces with several chemicals at different spatial locations usually requires multiple stamping and registration steps. Here, we describe an experimental method based on reaction–diffusion phenomena that allows for simultaneous micropatterning of a substrate with several coloured chemicals. In this method, called wet stamping (WETS), aqueous solutions of two or more inorganic salts are delivered onto a film of dry, ionically doped gelatin from an agarose stamp patterned in bas relief. Once in conformal contact, these salts diffuse into the gelatin, where they react to give deeply coloured precipitates. Separation of colours in the plane of the surface is the consequence of the differences in the diffusion coefficients, the solubility products, and the amounts of different salts delivered from the stamp, and is faithfully reproduced by a theoretical model based on a system of reaction–diffusion partial differential equations. The multicolour micropatterns are useful as non-binary optical elements, and could potentially form the basis of new applications in microseparations and in controlled delivery.},
  author       = {Klajn, Rafal and Fialkowski, Marcin and Bensemann, Igor T. and Bitner, Agnieszka and Campbell, C. J. and Bishop, Kyle and Smoukov, Stoyan and Grzybowski, Bartosz A.},
  issn         = {1476-4660},
  journal      = {Nature Materials},
  keywords     = {Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics, General Materials Science, General Chemistry},
  pages        = {729--735},
  publisher    = {Springer Nature},
  title        = {{Multicolour micropatterning of thin films of dry gels}},
  doi          = {10.1038/nmat1231},
  volume       = {3},
  year         = {2004},
}

@article{8525,
  abstract     = {Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points P n f grows with a period n faster than any following sequence of numbers {a n } n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented.},
  author       = {Kaloshin, Vadim},
  issn         = {0010-3616},
  journal      = {Communications in Mathematical Physics},
  keywords     = {Mathematical Physics, Statistical and Nonlinear Physics},
  pages        = {253--271},
  publisher    = {Springer Nature},
  title        = {{Generic diffeomorphisms with superexponential growth of number of periodic orbits}},
  doi          = {10.1007/s002200050811},
  volume       = {211},
  year         = {2000},
}

@article{8527,
  abstract     = {We introduce a new potential-theoretic definition of the dimension spectrum  of a probability measure for q > 1 and explain its relation to prior definitions. We apply this definition to prove that if  and  is a Borel probability measure with compact support in , then under almost every linear transformation from  to , the q-dimension of the image of  is ; in particular, the q-dimension of  is preserved provided . We also present results on the preservation of information dimension  and pointwise dimension. Finally, for  and q > 2 we give examples for which  is not preserved by any linear transformation into . All results for typical linear transformations are also proved for typical (in the sense of prevalence) continuously differentiable functions.},
  author       = {Hunt, Brian R and Kaloshin, Vadim},
  issn         = {0951-7715},
  journal      = {Nonlinearity},
  keywords     = {Mathematical Physics, General Physics and Astronomy, Applied Mathematics, Statistical and Nonlinear Physics},
  number       = {5},
  pages        = {1031--1046},
  publisher    = {IOP Publishing},
  title        = {{How projections affect the dimension spectrum of fractal measures}},
  doi          = {10.1088/0951-7715/10/5/002},
  volume       = {10},
  year         = {1997},
}