[{"abstract":[{"text":"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.","lang":"eng"}],"day":"21","publication_status":"published","page":"418-423","oa_version":"None","status":"public","date_updated":"2023-08-08T12:15:48Z","title":"One-step multilevel microfabrication by reaction−diffusion","external_id":{"pmid":["15620333"]},"publication":"Langmuir","scopus_import":"1","issue":"1","citation":{"ieee":"C. J. Campbell, R. Klajn, M. Fialkowski, and B. A. Grzybowski, “One-step multilevel microfabrication by reaction−diffusion,” <i>Langmuir</i>, vol. 21, no. 1. American Chemical Society, pp. 418–423, 2005.","chicago":"Campbell, Christopher J., Rafal Klajn, Marcin Fialkowski, and Bartosz A. Grzybowski. “One-Step Multilevel Microfabrication by Reaction−diffusion.” <i>Langmuir</i>. American Chemical Society, 2005. <a href=\"https://doi.org/10.1021/la0487747\">https://doi.org/10.1021/la0487747</a>.","ama":"Campbell CJ, Klajn R, Fialkowski M, Grzybowski BA. One-step multilevel microfabrication by reaction−diffusion. <i>Langmuir</i>. 2005;21(1):418-423. doi:<a href=\"https://doi.org/10.1021/la0487747\">10.1021/la0487747</a>","ista":"Campbell CJ, Klajn R, Fialkowski M, Grzybowski BA. 2005. One-step multilevel microfabrication by reaction−diffusion. Langmuir. 21(1), 418–423.","apa":"Campbell, C. J., Klajn, R., Fialkowski, M., &#38; Grzybowski, B. A. (2005). One-step multilevel microfabrication by reaction−diffusion. <i>Langmuir</i>. American Chemical Society. <a href=\"https://doi.org/10.1021/la0487747\">https://doi.org/10.1021/la0487747</a>","short":"C.J. Campbell, R. Klajn, M. Fialkowski, B.A. Grzybowski, Langmuir 21 (2005) 418–423.","mla":"Campbell, Christopher J., et al. “One-Step Multilevel Microfabrication by Reaction−diffusion.” <i>Langmuir</i>, vol. 21, no. 1, American Chemical Society, 2005, pp. 418–23, doi:<a href=\"https://doi.org/10.1021/la0487747\">10.1021/la0487747</a>."},"date_published":"2005-01-21T00:00:00Z","_id":"13432","author":[{"last_name":"Campbell","full_name":"Campbell, Christopher J.","first_name":"Christopher J."},{"first_name":"Rafal","full_name":"Klajn, Rafal","id":"8e84690e-1e48-11ed-a02b-a1e6fb8bb53b","last_name":"Klajn"},{"first_name":"Marcin","full_name":"Fialkowski, Marcin","last_name":"Fialkowski"},{"first_name":"Bartosz A.","full_name":"Grzybowski, Bartosz A.","last_name":"Grzybowski"}],"type":"journal_article","year":"2005","publisher":"American Chemical Society","doi":"10.1021/la0487747","language":[{"iso":"eng"}],"volume":21,"article_type":"original","publication_identifier":{"issn":["0743-7463"],"eissn":["1520-5827"]},"quality_controlled":"1","month":"01","intvolume":"        21","keyword":["Electrochemistry","Spectroscopy","Surfaces and Interfaces","Condensed Matter Physics","General Materials Science"],"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","pmid":1,"date_created":"2023-08-01T10:38:29Z"},{"doi":"10.1038/nmat1231","language":[{"iso":"eng"}],"year":"2004","publisher":"Springer Nature","type":"journal_article","author":[{"first_name":"Rafal","full_name":"Klajn, Rafal","last_name":"Klajn","id":"8e84690e-1e48-11ed-a02b-a1e6fb8bb53b"},{"last_name":"Fialkowski","first_name":"Marcin","full_name":"Fialkowski, Marcin"},{"full_name":"Bensemann, Igor T.","first_name":"Igor T.","last_name":"Bensemann"},{"last_name":"Bitner","first_name":"Agnieszka","full_name":"Bitner, Agnieszka"},{"last_name":"Campbell","first_name":"C. J.","full_name":"Campbell, C. J."},{"full_name":"Bishop, Kyle","first_name":"Kyle","last_name":"Bishop"},{"first_name":"Stoyan","full_name":"Smoukov, Stoyan","last_name":"Smoukov"},{"last_name":"Grzybowski","full_name":"Grzybowski, Bartosz A.","first_name":"Bartosz A."}],"_id":"13435","date_published":"2004-09-19T00:00:00Z","date_created":"2023-08-01T10:39:23Z","pmid":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","article_processing_charge":"No","intvolume":"         3","keyword":["Mechanical Engineering","Mechanics of Materials","Condensed Matter Physics","General Materials Science","General Chemistry"],"month":"09","publication_identifier":{"eissn":["1476-4660"],"issn":["1476-1122"]},"quality_controlled":"1","volume":3,"article_type":"original","date_updated":"2023-08-08T12:42:51Z","status":"public","day":"19","publication_status":"published","oa_version":"None","page":"729-735","abstract":[{"lang":"eng","text":"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."}],"citation":{"chicago":"Klajn, Rafal, Marcin Fialkowski, Igor T. Bensemann, Agnieszka Bitner, C. J. Campbell, Kyle Bishop, Stoyan Smoukov, and Bartosz A. Grzybowski. “Multicolour Micropatterning of Thin Films of Dry Gels.” <i>Nature Materials</i>. Springer Nature, 2004. <a href=\"https://doi.org/10.1038/nmat1231\">https://doi.org/10.1038/nmat1231</a>.","ieee":"R. Klajn <i>et al.</i>, “Multicolour micropatterning of thin films of dry gels,” <i>Nature Materials</i>, vol. 3. Springer Nature, pp. 729–735, 2004.","short":"R. Klajn, M. Fialkowski, I.T. Bensemann, A. Bitner, C.J. Campbell, K. Bishop, S. Smoukov, B.A. Grzybowski, Nature Materials 3 (2004) 729–735.","apa":"Klajn, R., Fialkowski, M., Bensemann, I. T., Bitner, A., Campbell, C. J., Bishop, K., … Grzybowski, B. A. (2004). Multicolour micropatterning of thin films of dry gels. <i>Nature Materials</i>. Springer Nature. <a href=\"https://doi.org/10.1038/nmat1231\">https://doi.org/10.1038/nmat1231</a>","mla":"Klajn, Rafal, et al. “Multicolour Micropatterning of Thin Films of Dry Gels.” <i>Nature Materials</i>, vol. 3, Springer Nature, 2004, pp. 729–35, doi:<a href=\"https://doi.org/10.1038/nmat1231\">10.1038/nmat1231</a>.","ista":"Klajn R, Fialkowski M, Bensemann IT, Bitner A, Campbell CJ, Bishop K, Smoukov S, Grzybowski BA. 2004. Multicolour micropatterning of thin films of dry gels. Nature Materials. 3, 729–735.","ama":"Klajn R, Fialkowski M, Bensemann IT, et al. Multicolour micropatterning of thin films of dry gels. <i>Nature Materials</i>. 2004;3:729-735. doi:<a href=\"https://doi.org/10.1038/nmat1231\">10.1038/nmat1231</a>"},"scopus_import":"1","publication":"Nature Materials","title":"Multicolour micropatterning of thin films of dry gels","external_id":{"pmid":["15378052"]}},{"month":"04","publication_identifier":{"issn":["0010-3616","1432-0916"]},"quality_controlled":"1","publication":"Communications in Mathematical Physics","title":"Generic diffeomorphisms with superexponential growth of number of periodic orbits","article_type":"original","volume":211,"date_created":"2020-09-18T10:50:20Z","citation":{"chicago":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2000. <a href=\"https://doi.org/10.1007/s002200050811\">https://doi.org/10.1007/s002200050811</a>.","ieee":"V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number of periodic orbits,” <i>Communications in Mathematical Physics</i>, vol. 211. Springer Nature, pp. 253–271, 2000.","short":"V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.","ista":"Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.","mla":"Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits.” <i>Communications in Mathematical Physics</i>, vol. 211, Springer Nature, 2000, pp. 253–71, doi:<a href=\"https://doi.org/10.1007/s002200050811\">10.1007/s002200050811</a>.","apa":"Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of number of periodic orbits. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s002200050811\">https://doi.org/10.1007/s002200050811</a>","ama":"Kaloshin V. Generic diffeomorphisms with superexponential growth of number of periodic orbits. <i>Communications in Mathematical Physics</i>. 2000;211:253-271. doi:<a href=\"https://doi.org/10.1007/s002200050811\">10.1007/s002200050811</a>"},"extern":"1","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       211","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"author":[{"last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim","first_name":"Vadim"}],"_id":"8525","day":"01","date_published":"2000-04-01T00:00:00Z","page":"253-271","publication_status":"published","oa_version":"None","abstract":[{"text":"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.","lang":"eng"}],"doi":"10.1007/s002200050811","language":[{"iso":"eng"}],"year":"2000","publisher":"Springer Nature","date_updated":"2021-01-12T08:19:52Z","status":"public","type":"journal_article"},{"month":"06","publication_identifier":{"issn":["0951-7715","1361-6544"]},"quality_controlled":"1","publication":"Nonlinearity","title":"How projections affect the dimension spectrum of fractal measures","article_type":"original","volume":10,"date_created":"2020-09-18T10:50:41Z","citation":{"ama":"Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. 1997;10(5):1031-1046. doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>","apa":"Hunt, B. R., &#38; Kaloshin, V. (1997). How projections affect the dimension spectrum of fractal measures. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>","short":"B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.","mla":"Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>, vol. 10, no. 5, IOP Publishing, 1997, pp. 1031–46, doi:<a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">10.1088/0951-7715/10/5/002</a>.","ista":"Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of fractal measures. Nonlinearity. 10(5), 1031–1046.","ieee":"B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum of fractal measures,” <i>Nonlinearity</i>, vol. 10, no. 5. IOP Publishing, pp. 1031–1046, 1997.","chicago":"Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum of Fractal Measures.” <i>Nonlinearity</i>. IOP Publishing, 1997. <a href=\"https://doi.org/10.1088/0951-7715/10/5/002\">https://doi.org/10.1088/0951-7715/10/5/002</a>."},"issue":"5","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","extern":"1","intvolume":"        10","keyword":["Mathematical Physics","General Physics and Astronomy","Applied Mathematics","Statistical and Nonlinear Physics"],"author":[{"first_name":"Brian R","full_name":"Hunt, Brian R","last_name":"Hunt"},{"orcid":"0000-0002-6051-2628","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","first_name":"Vadim"}],"_id":"8527","day":"19","date_published":"1997-06-19T00:00:00Z","page":"1031-1046","oa_version":"None","publication_status":"published","abstract":[{"lang":"eng","text":"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."}],"doi":"10.1088/0951-7715/10/5/002","language":[{"iso":"eng"}],"year":"1997","publisher":"IOP Publishing","date_updated":"2021-01-12T08:19:53Z","status":"public","type":"journal_article"}]