Arizona Center for

Mathematical Sciences

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The Arizona Center for Mathematical Sciences is an interdisciplinary research group with in the Department of Mathematics at the University of Arizona in Tucson, Arizona. ACMS enjoys close ties with the Departments of Physics and Optical Sciences.


About ACMS

The primary goal of ACMS is to provide an environment for research and learning in the Mathematical Sciences. Its basic research themes are the modeling, understanding and applicability of nonlinear processes in optics, fluids, neural networks, and random distributed systems with continuing investigations into pattern dynamics, percolation, behavior of lattice gasses, nonlinear stability, low dimensional chaos, turbulence, dynamical systems and the nature of integrable systems of differential equations.

Research and learning takes place at all levels. The breadth of activity and spectrum of interest and talent among visiting colleagues serves to stimulate interdisciplinary work and promote the cross fertilization of ideas. Graduate students interested in applied mathematics enjoy a unique environment in which they can experience first hand the unity in the approaches (modeling, simulation, analysis, and involvement in experiments) with which mathematical scientists tackle a diverse set of problems from all areas of the physical sciences. There are several ongoing weekly working seminars in addition to regular departmental colloquia; these are in the areas of applied analysis, computation, dynamical systems, nonlinear optics, neural networks, integrable systems, and mathematical physics.

Nonlinear Optics has attained a special status at ACMS and the exceptional multidisciplinary culture at the University of Arizona provides a unique environment for collaborative research withcolleages at the Optical Sciences Center and the Program in Applied Mathematics. Graduate students in Applied Mathematics, Optical Sciences and Physics work together on research projects at the frontiers of this exciting field. Tucson's designation as Optics Valley" reflects the large concentration of optics industries in the region and provides a strong industrial link to the University of Arizona.


Computing Facilities

The Arizona Center for Mathematical Sciences (ACMS) is a recognized world leader in the numerical simulation of linear and nonlinear optical interactions. The ACMS possesses a dedicated in-house supercomputing laboratory that provides high performance computing, storage, and visualization resources for its researchers. The primary computing hardware consist of a SGI UV2000, a SGI Altix XE Cluster, a 60 processor AMD Opteron cluster and a range of high performance nVidia GPU equipped visualization workstations and multi GPU equipped compute servers. more...


Experimental Facilities

Since October of 2007, the ACMS research program on femtosecond light strings includes an experimental component. These experiments are conducted in a new Terawatt laser facility collocated with the ACMS at the College of Optical Sciences, University of Arizona. The experimental facility is equipped with a 35mJ femtosecond laser system, high-energy Optical Parametric Amplifier (OPA) and various pieces of equipment for pulse and beam shaping and diagnostics.



ACMS is located on the fifth floor of the Meinel Optical Sciences Building #94. The University of Arizona’s new Meinel Optical Sciences Building received a 2007 American Institute of Architects (AIA) Honor Award for Architecture, the profession’s highest recognition of works that exemplify excellence in architecture, interior design and urban planning. It was one of only 11 buildings worldwide selected this year and the only Tucson building to ever receive an honor award in the award’s 59-year history.

Meinel Optical Sciences Bldg.,
1630 E University Blvd.,
5th Floor,
University of Arizona
Tucson, AZ 85721-0094

Contact us

Department of Mathematics
617 N. Santa Rita
University of Arizona
Tucson, AZ 85721-0089
Phone: (520) 621-8129 Fax: (520) 621-1510


Current News and Events


Cork School 2013

The Cork School 2013 was hosted by the Arizona Centre for Mathematical Sciences and University College Cork. The school was intended for graduate students, advanced undergraduate students and even senior researchers seeking an accelerated exposure to theory and mathematics describing ultrashort pulse propagation.

Description: Extreme nonlinear optical events associated with filamentation of ultrashort laser pulses involving unconventional beam profiles in transparent gaseous and solid state media, require a fundamental understanding of nonlinear saturation, nonequilibrium plasma generation and ultra-fast light matter coupling.

Location: University College Cork, Ireland

Dates: July 28, 2013 - August 2, 2013



School Poster (PDF format)


click here to view Cork School 2013 website

Some feedback from this year's students:

"Thank you for a wonderful experience."

"The lectures were excellent."

"The lectures were so well planned and sequenced. The vital laser codes were well explained and provided - extremely generous. Each lecturer was excellent."

01-12-2012: New ACMS supercomputer goes on-line.

Having completed initial testing and verification ACMS newest numerical simulation platform goes "on-line" and is now available to ACMS researchers. This latest generation computer, a scalable, coherent shared memory SGI® UV™ 2000 computer, was first released to the public in June 2012 and installed at the ACMS in September 2012.

The SGI UV 2000 enables the ACMS to solve multi-terabyte problems, making it the ideal platform to accelerate our leading edge research in the numerical simulation of linear and nonlinear optical interactions.

The SGI UV 2000 features the latest Intel® Xeon® processor E5 product family and runs unmodified, off-the-shelf Linux® software. SGI UV 2000 also supports Intel's many integrated cores (MIC) technology as well as nVidia® Quadro® GPUs and Tesla® Accelerators. more...

News Archive


08-09-2010: $7.5M Laser Research Project

ACMS has won a new five-year, $7.5 million U.S Department of Defense grant to fund the project, "Propagation of Ultrashort Laser Pulses Through Transparent Media." More details available here and here. The multidisciplinary university research initiative grant has the University of Arizona as the lead institution with five external universities as partners. The focus of the MURI project is to gain a fundamental understanding of all physical processes involved in the propagation of ultra-intense femtosecond laser pulses through the atmosphere with the aim of designing new forms of robust laser beams that can propagate over much longer distances than conventional beams. Applications of this novel atmospheric "light-string" are many and varied including: femtosecond atmospheric LIDAR and remote detection of pollutants, explosive, chem./bio agents; artificial guidestar for turbulence correction in astronomy, remote plasma generation for Laser Induced Breakdown Spectroscopy (LIBS) and redirection of lighting strikes.

The assembled MURI team consists of a core applied mathematics and theoretical physics (Moloney, Kolesik, Wright, Newell, Glasner, Brio, Venkataramani) and experimental femtosecond optics (Polynkin) at ACMS and external theoretical physicists Becker and Jaron-Becker at JILA, University of Colorado, Christodoulides (Central Florida) and experimentalists Murnane, Kapetyn (University of Colorado), Levis (Temple), Gaeta (Cornell) and Durfee (Colorado School of Mines).

The MURI team will maintain strong collaborative links with Air Force Research scientists (Roach at AFRL Kirtland and Albanese (Brooks City AFB) and with leading European and Canadian research groups working in the field.

03-25-2010: Ultrafast Nonlinear Optics on Macroscopic and Sub-Wavelength Scales

The ACMS has received approval of their recent proposal Ultrafast Nonlinear Optics on Macroscopic and Sub-Wavelength Scales. This proposal addresses contemporary problems in the study of nonlinear optics on scales that are both much larger and much smaller than the wavelength of light. On macroscopic scales, we propose to study extreme nonlinear optics associated with ultra-short pulse propagation in extended media such as air, gases and condensed matter. Even at this level, the light matter interaction requires a microscopic quantum description. Another important open problem is the nature of lasing at multiple wavelengths in vertical external cavity surface emitting lasers (VECSELs), these devices have recently been shown by us to emit THz waves at room temperature and at power levels six orders of magnitude stronger than the much touted quantum cascade lasers.

A major challenge is the incorporation of the full many-body microscopic description in a multi-pass laser propagation problem. Past implementations have been restricted to single pass ultrashort pulse propagation through a single stack of quantum wells. The other extreme, we propose to study linear and nonlinear optics on sub-wavelength scales, the field of near-field optics. Recent developments in nanophotonics, plasmonics and metamaterials raise fundamental questions regarding the physics of light interaction with materials and with numerical approaches being implemented to study these phenomena. At the Arizona Center for Mathematical Sciences we have been developing computer codes that implement both time domain and frequency-domain, 3D Maxwell solvers.



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Meinel Optical Sciences Bldg., 5th Floor, University of Arizona - Tucson, AZ 85721-0094 *** T. 520 621 8129 *** F. 520 621 1510 *** *** Copyright 2010. All Rights Reserved.