---
_id: '13432'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Christopher J.
full_name: Campbell, Christopher J.
last_name: Campbell
- 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
citation:
ama: Campbell CJ, Klajn R, Fialkowski M, Grzybowski BA. One-step multilevel microfabrication
by reaction−diffusion. Langmuir. 2005;21(1):418-423. doi:10.1021/la0487747
apa: Campbell, C. J., Klajn, R., Fialkowski, M., & Grzybowski, B. A. (2005).
One-step multilevel microfabrication by reaction−diffusion. Langmuir. American
Chemical Society. https://doi.org/10.1021/la0487747
chicago: Campbell, Christopher J., Rafal Klajn, Marcin Fialkowski, and Bartosz A.
Grzybowski. “One-Step Multilevel Microfabrication by Reaction−diffusion.” Langmuir.
American Chemical Society, 2005. https://doi.org/10.1021/la0487747.
ieee: C. J. Campbell, R. Klajn, M. Fialkowski, and B. A. Grzybowski, “One-step multilevel
microfabrication by reaction−diffusion,” Langmuir, vol. 21, no. 1. American
Chemical Society, pp. 418–423, 2005.
ista: Campbell CJ, Klajn R, Fialkowski M, Grzybowski BA. 2005. One-step multilevel
microfabrication by reaction−diffusion. Langmuir. 21(1), 418–423.
mla: Campbell, Christopher J., et al. “One-Step Multilevel Microfabrication by Reaction−diffusion.”
Langmuir, vol. 21, no. 1, American Chemical Society, 2005, pp. 418–23,
doi:10.1021/la0487747.
short: C.J. Campbell, R. Klajn, M. Fialkowski, B.A. Grzybowski, Langmuir 21 (2005)
418–423.
date_created: 2023-08-01T10:38:29Z
date_published: 2005-01-21T00:00:00Z
date_updated: 2023-08-08T12:15:48Z
day: '21'
doi: 10.1021/la0487747
extern: '1'
external_id:
pmid:
- '15620333'
intvolume: ' 21'
issue: '1'
keyword:
- Electrochemistry
- Spectroscopy
- Surfaces and Interfaces
- Condensed Matter Physics
- General Materials Science
language:
- iso: eng
month: '01'
oa_version: None
page: 418-423
pmid: 1
publication: Langmuir
publication_identifier:
eissn:
- 1520-5827
issn:
- 0743-7463
publication_status: published
publisher: American Chemical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: One-step multilevel microfabrication by reaction−diffusion
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2005'
...
---
_id: '13435'
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.
article_processing_charge: No
article_type: original
author:
- 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: Igor T.
full_name: Bensemann, Igor T.
last_name: Bensemann
- first_name: Agnieszka
full_name: Bitner, Agnieszka
last_name: Bitner
- first_name: C. J.
full_name: Campbell, C. J.
last_name: Campbell
- first_name: Kyle
full_name: Bishop, Kyle
last_name: Bishop
- first_name: Stoyan
full_name: Smoukov, Stoyan
last_name: Smoukov
- first_name: Bartosz A.
full_name: Grzybowski, Bartosz A.
last_name: Grzybowski
citation:
ama: Klajn R, Fialkowski M, Bensemann IT, et al. Multicolour micropatterning of
thin films of dry gels. Nature Materials. 2004;3:729-735. doi:10.1038/nmat1231
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. Nature Materials. Springer Nature. https://doi.org/10.1038/nmat1231
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.” Nature Materials. Springer
Nature, 2004. https://doi.org/10.1038/nmat1231.
ieee: R. Klajn et al., “Multicolour micropatterning of thin films of dry
gels,” Nature Materials, vol. 3. Springer Nature, pp. 729–735, 2004.
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.
mla: Klajn, Rafal, et al. “Multicolour Micropatterning of Thin Films of Dry Gels.”
Nature Materials, vol. 3, Springer Nature, 2004, pp. 729–35, doi:10.1038/nmat1231.
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.
date_created: 2023-08-01T10:39:23Z
date_published: 2004-09-19T00:00:00Z
date_updated: 2023-08-08T12:42:51Z
day: '19'
doi: 10.1038/nmat1231
extern: '1'
external_id:
pmid:
- '15378052'
intvolume: ' 3'
keyword:
- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics
- General Materials Science
- General Chemistry
language:
- iso: eng
month: '09'
oa_version: None
page: 729-735
pmid: 1
publication: Nature Materials
publication_identifier:
eissn:
- 1476-4660
issn:
- 1476-1122
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Multicolour micropatterning of thin films of dry gels
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2004'
...
---
_id: '8525'
abstract:
- lang: eng
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.
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Kaloshin V. Generic diffeomorphisms with superexponential growth of number
of periodic orbits. Communications in Mathematical Physics. 2000;211:253-271.
doi:10.1007/s002200050811
apa: Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of
number of periodic orbits. Communications in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s002200050811
chicago: Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth
of Number of Periodic Orbits.” Communications in Mathematical Physics.
Springer Nature, 2000. https://doi.org/10.1007/s002200050811.
ieee: V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number
of periodic orbits,” Communications in Mathematical Physics, vol. 211.
Springer Nature, pp. 253–271, 2000.
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.” Communications in Mathematical Physics, vol. 211,
Springer Nature, 2000, pp. 253–71, doi:10.1007/s002200050811.
short: V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.
date_created: 2020-09-18T10:50:20Z
date_published: 2000-04-01T00:00:00Z
date_updated: 2021-01-12T08:19:52Z
day: '01'
doi: 10.1007/s002200050811
extern: '1'
intvolume: ' 211'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '04'
oa_version: None
page: 253-271
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Generic diffeomorphisms with superexponential growth of number of periodic
orbits
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 211
year: '2000'
...
---
_id: '8527'
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.
article_processing_charge: No
article_type: original
author:
- first_name: Brian R
full_name: Hunt, Brian R
last_name: Hunt
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal
measures. Nonlinearity. 1997;10(5):1031-1046. doi:10.1088/0951-7715/10/5/002
apa: Hunt, B. R., & Kaloshin, V. (1997). How projections affect the dimension
spectrum of fractal measures. Nonlinearity. IOP Publishing. https://doi.org/10.1088/0951-7715/10/5/002
chicago: Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension
Spectrum of Fractal Measures.” Nonlinearity. IOP Publishing, 1997. https://doi.org/10.1088/0951-7715/10/5/002.
ieee: B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum
of fractal measures,” Nonlinearity, vol. 10, no. 5. IOP Publishing, pp.
1031–1046, 1997.
ista: Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of
fractal measures. Nonlinearity. 10(5), 1031–1046.
mla: Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum
of Fractal Measures.” Nonlinearity, vol. 10, no. 5, IOP Publishing, 1997,
pp. 1031–46, doi:10.1088/0951-7715/10/5/002.
short: B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.
date_created: 2020-09-18T10:50:41Z
date_published: 1997-06-19T00:00:00Z
date_updated: 2021-01-12T08:19:53Z
day: '19'
doi: 10.1088/0951-7715/10/5/002
extern: '1'
intvolume: ' 10'
issue: '5'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa_version: None
page: 1031-1046
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: How projections affect the dimension spectrum of fractal measures
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10
year: '1997'
...