Michael J. Shelley - US grants

9320154 Shelley A color graphics workstation, with accessories and software, will be acquired to advance research projects, all involving large-scale multi-dimensional scientific computation, in computational fluid dynamics, physics, nonlinear optics, and biology. One research project will use computer visualization and animation to comprehend large-scale simulations of complex fluid flows, develop good numerical methods for such problems, and to disseminate these results to the scientific community. These problems include computation and modeling of topology transitions and singularity formation in fluid flows (vortex reconnection and bubble formation), and computation of multi-phase flows with surface tensions. Another research project will apply computer graphics to research on computer simulation of the heart. It will be used to construct and improve the heart model, to debug the code, to visualize the resulting computer experiments, to compare the simulational results with experimental observations, and to communicate the results to others. Comprehending the heart model involves simultaneous visualization of a deformable structure and the fluid it contains, all requiring the rapid manipulation of massive amounts of data. A third project will make numerical studies of magnetic structures in two-dimensional unsteady flow fields. At large magnetic Reynolds numbers, small-scale structures associated with fast dynamo action in stretching flows will be identified, and comparisons made with theoretical dynamo models. Color-coding of field strength and studying the field evolution using videotaped se quences at about 60 frames/cycle, should allow direct determination of the mechanism of field amplification. Finally, research will be done on computational investigations addressing current issues of spatial complexity in 3-d nonlinear optical systems. One computational study is of mathematical models for the nonlinear evolution of self-focused laser beams in systems which do not display transverse collapse. In some cases, the beam profiles develop multiple filaments, corroborating experimental observations of these finely-interwoven optical structures will be considerably enhanced by fully three-dimensional computer visualizations. *** ECEXE @ j i SSMARQUESCR @ j B SSMYST SCR @ j L SSSTARS SCR @ j D TADA WAV @ j & l TARTAN BMP @ j 4 v TERMINALEXE @ j E B TERMINALHLP @ j 9320154 Shelley A color graphics workstation, with accessories and software, will be acquired to advance research projects, | ^ ` o q \ ^ w | $ $ $ G | | Times Symbol " Helvetica Chicago Times New Roman & Arial 5 Courier New R ZapfDingbats Palatino Greek GenMath MathMeteor MT Extra " e e 4 Shelley/NYU Mark Purvis Mark Purvis

This is a proposal to modernize the computer network and the display terminals used by researchers of the Courant Institute in order to support research using high-performance computers and to support high-performance visualization methods in computer and information science and engineering research.

9707494 Michael Shelley These projects concern dynamics and pattern formation in complex fluids, and singularity formation and topological transitions in Newtonian fluids. The first project considers the hydrodynamics of slender elastic filaments, such as arise in liquid crystal flows, the dynamics of phospho-lipid bilayer tubes, and in the dynamics of biological polymers. Building tractable computational models, that account for hydrodynamic interactions of the filament with itself, relies on discriminating exploitation of slenderness. This still gives a computationally intensive problem with high-order time-step constraints from elasticity, interaction integrals with singular kernels, and integral equations to be solved at every time-step. The second project continues towards an understanding of topological transitions of fluid/fluid interfaces between immiscible liquids. The fundamental questions are: How does surface tension provoke or mediate transitions? What characterizes the singularity? What physics needs to be added to follow the transition? And what is left of the singularity in its aftermath? Building upon previous work on such singularities in the Kelvin-Helmholtz instability between immiscible fluids, it is proposed to study, computationally and analytically, singularities and transitions in jets that separate immiscible fluids, both by using sharp interface models, and fluid models that have viscosity and allow some miscibility. The third project studies the effect of shear-thinning, a property shared with many non-Newtonian fluids and liquid crystal flows, on the development of the Saffman-Taylor instability. Some of the modelling work has already been done, yielding a natural non-Newtonian version of Darcy's law, relating the fluid velocity to the solution of a nonlinear elliptic problem. It is proposed to now simulate the full nonlinear dynamics of such a bubble expanding into a shear-thinning liquid. This is a very challenging comp utational problem as it involves the solution of nonlinear elliptic problems on an evolving domain. Much of the fundamental dynamics of fluids and materials -- singularity and pattern formation are two central examples -- will be understood by a progression from mathematical modelling, to developing computational methods and relevant mathematical understanding, and thence to large-scale simulation and data analysis through high-performance computing. The three projects to be pursued here all lie at the intersection of fluid dynamics and materials science, and all illustrate the above statement. In the first project, it is proposed to understand and simulate the dynamics of filamentary structures, as arise in phase transitions of liquid crystalline fluids, the dynamics of phospho-lipid bilayer tubes, and in the dynamics of biological polymers. In first example, such filaments are of potential technological importance in the manufacture of high-strength filaments. The second project continues towards a theoretical understanding of what drives the break-up into droplets of a jet of fluid into a second, different fluid (say, oil and water). While easy and common to observe, such behavior is strongly associated with surface tension, an effect that is still ill-understood, and yet lies at the heart of much basic fluid phenomena. This will be studied by a combination of modelling, analysis, and large-scale computation. The final project concerns the dynamics of shear-thinning liquids flowing in thin gaps. Such flows are important to display device design, and to injection molding. Of particular interest is the instability and pattern formation associated with a gas/liquid interface which is driven but mediated by surface tension. This is an extremely challenging computational problem, requiring the development of new simulational methods.

This MRI award will support the purchase of equipment for research, research training, and education in computational fluid dynamics and visualization, at the Courant Institute. The aim is to create a state-of-the-art simulation and visualization center within our new Applied Mathematics Laboratory (AML), which is dedicated to education and research training in fluid dynamical simulation and visualization. The equipment will be shared by research groups engaged in various areas of fluid dynamics research at the Institute, and integrated with the present and future computational and visualization facilities owned by these research groups. The planned instrumentation includes computers, a mass storage system, projection facilities, network enhancements, third-party software licenses, and miscellaneous smaller items. . The research and research training to be conducted in the facility is dedicated to understanding complicated fluid flows - 2- and 3-dimensional - arising in biophysics, geophysics, and energy research as well as basic fluid dynamics, and to education in fluid dynamical computation and visualization. A major beneficiary of the requested instrumentation is the new Applied Mathematics Laboratory now under construction on the ground floor of Warren Weaver Hall. The AML is comprised of two components, the Wetlab and the ViSLab. The Wetlab is a demonstration and research laboratory of fluid mechanics. The ViSLab (Visualization and Simulation Laboratory) is the associated computational facility. The AML facility is designed to integrate research with research training and education, and to synthesize computation, visualization, and experimental research with research training and instruction. Research activities that will use the proposed instrumentation include the simulation of insect flight, computational studies of the dynamics of complex fluids, the fluid dynamics of the heart, three-dimensional niagnetohydrodynamic modelling for fusion science and solar physics, geophysical flows, and study of aerodynamic flow in complicated geometry. Through the present proposal it will provide our students with access to large-scale simulation platforms and to modern visualization and animation hardware and software. This research effort will be funded jointly by the Division of Mathematical Science, the MPS Office of Multidisciplinary Activities, and the MRI Program.

Peskin
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Unsteady fluid flows driven by dynamic boundaries are among
the most difficult flows to simulate and visualize. Whether
drawn from polymer rheology, microflight, or cardiac fluid
dynamics, these problems involve structures on many length and
time scales, strong coupling between the fluid and a deformable
boundary, and complex geometry. The investigator and his
colleagues, taking the problems of insect flight and heart
function as focal points for a multidisciplinary collaboration,
seek a new paradigm for understanding boundary-fluid dynamics.
This new paradigm involves both numerical simulation and
experimental investigation, brought together through the emerging
technology of virtual reality. On the numerical side, they
develop new adaptive and hierarchical numerical techniques, as
well as improve existing methods (immersed boundary and adaptive
grid), to enable interactive simulation experiments and steerable
computation. The experimental program focuses both on methods
that can be used to validate and complement the results of
numerical simulations, and on novel techniques for the study of
unsteady flows with dynamic boundaries. Computational and
experimental approaches are integrated within a virtual
environment that enables a researcher to modify interactively the
parameters and geometry of the simulated system, steer
computational processes, flexibly visualize experimental data,
and use experimental data to guide computation.
When unsteady three-dimensional flows interact with dynamic
boundaries such as heart valves and insect wings, the resulting
fluid dynamics defy easy representation and conventional
analysis. The tight coupling between boundary and fluid, the
differing and interacting length and time scales, and the
complexity of turbulent motions make these problems a formidable
theoretical and computational challenge. Breakthroughs in
understanding this class of problems will enable important
advances in fields such as medicine, biology, aeronautics, and
chemical engineering. Achieving such breakthroughs is the goal of
a collaboration between researchers from NYU's Courant Institute
of Mathematical Sciences (CIMS) and the University of Washington
(UW), with combined expertise in mathematics and computation,
experimental laboratory investigation, and scientific
visualization. Heart valve function and insect flight cannot be
explained by classical arguments based on steady flow. Millions
of years of evolution have produced shapes, feedback mechanisms,
and boundary properties in response to the complexity of the
boundary-fluid interaction. A greater understanding of these
interactions between boundary and flow will open the door to new
generations of artificial heart valves, small and highly
efficient flying machines, and other devices carefully designed
to interact with the complex but repeatable behaviors of boundary
dominated fluid flows. A key goal of this project is the
integration of experiment and computation in a virtual
environment that facilitates the involvement of the human
investigator. The project strives to change the paradigm of
research in this area. A researcher should be able to modify the
parameters and geometry of a simulated system while the
simulation is running; to steer, for a given simulated system,
the computational process itself; to use experimental data to
guide the computation; and to process and interact with the
experimental data, while visualizing it in three dimensions as
well as over time. While the focus is on the core studies of
insect flight and heart function, extrapolation from these core
examples should enable breakthroughs wherever fluids (including
gases) interact with structures of complicated and possibly
dynamic geometry. This KDI project is supported by the Division
of Mathematical Sciences, the Division of Integrative Biology and
Neuroscience, and the Division of Chemical and Transport Systems.

Many achievements in the biological and biomedical sciences are fueled by advances in technology and computational science. To address the complex challenges in the biological sciences in the 21st century, there is a growing need for professionals who can translate scientific problems in biology into mathematics and computations; for such productive work, familiarity with modern scientific computing approaches as well as key biological challenges is essential.

Intellectual Merit: This IGERT award is for a multidisciplinary Computational Biology (COB) doctoral program at NYU and MSSM targeting students interested in pursuing research in biology/biomedicine who require a transition from/to the mathematical/computer/physical sciences to best meet scientific challenges and career goals. This experimental, bidirectional program will offer integrative training that exploits NYU's strengths in applied mathematics, computer science, biology, and biochemistry, and Sinai's leadership in biomedicine. The major COB research themes - macromolecular modeling, computational genomics, and physiological modeling - will train students to investigate biological systems spanning wide temporal and spatial scales, from atoms and macromolecules, to cells and organs, to organisms. Modeling biological systems across such scales is essential for a modern systems biology approach aimed at understanding physiological processes and diseases and applying this knowledge to biomedicine.

To integrate training in biological and computational areas and provide trainees broad scientific perspectives and work experiences, the COB PhD program includes: (1) Dual faculty mentorship for thesis research; (2) Interdisciplinary training through flexible and background-tailored tracks in scientific computing and computational biology (courses in computer science, applied mathematics, biology, and biomedicine), trainee-led seminars, and ethics/research conduct courses, while ensuring competitive time to degree (5 years); (3) Summer internships in industry, academia, government (Agilent, IBM, Celera, Merck, Novasite and 3D Pharmaceuticals, supercomputing centers), or international laboratories; (4) Learning environments and activities that promote interdisciplinary interactions and broader collaborations within and outside NYU/MSSM, including: trainee-led COB seminars, annual COB retreat, and common COB lab/lounge; and (5) Mentoring and career development activities to ensure student retention, especially women and underrepresented groups, through student advisory committees, trainee-led support group, and partnerships with Burroughs Wellcome Fund and NYC's IGERT programs at CUNY and Columbia. The COB doctoral program will be evaluated and evolved continuously by its executive and internal/external advisors in close collaboration with the pedagogical experts of NYU's Center for Teaching Excellence (CTE).

Broader Impacts: COB will train math/computer science students to successfully model biological systems and, in turn, provide biology students the grounding in computational techniques so they can tailor the model and algorithms to specific biological problems. To help bridge disciplinary gaps, we will design background-tailored short (non-credit) courses before Year 1 and promote peer learning by pairing students from complementary backgrounds. We expect that COB's activities will enable trainees to act as catalysts for novel interdisciplinary collaborations and to acquire expertise in cutting-edge research areas; these experiences will prepare them uniquely for research and education careers in academia, industry, and government. In addition, COB's program of integrating scientific grounding, experience in team-oriented multidisciplinary projects, mentoring, and career broadening activities will serve as a new model of graduate training at NYU/MSSM and beyond, promote the development of curricula for computational biology, and provide the opportunity to develop the COB doctoral degree at NYU based on the new model. Recognizing the urgent need for diversity in the sciences, we will make concerted efforts in conjunction with participating departments and with successful new minority initiatives at NYU to recruit and retain the brightest students, especially women and other underrepresented groups.

IGERT is an NSF-wide program intended to meet the challenges of educating U.S. Ph.D. scientists and engineers with the interdisciplinary background, deep knowledge in a chosen discipline, and the technical, professional, and personal skills needed for the career demands of the future. The program is intended to catalyze a cultural change in graduate education by establishing innovative new models for graduate education and training in a fertile environment for collaborative research that transcends traditional disciplinary boundaries. In this sixth year of the program, awards are being made to institutions for programs that collectively span the areas of science and engineering supported by NSF.

The investigators will develop robust, accurate, and cost-effective
methods for simulating the dynamics of suspensions of flexible fibers
in a Stokesian fluid. Flexible fibers make up the
micro-structure of suspensions that show strongly non-Newtonian bulk
behavior, such as elasticity, shear-thinning, and normal stresses
differences in shear flows. By taking a nonstandard approach to this
problem, and designing a numerical algorithm based on a nonlocal
slender-body approximation to hydrodynamical interactions, it is
possible to simulate problems not feasible with standard methods. As
this numerical method has a firm mathematical foundation, method
design can be approached as a numerical analysis problem, carefully
treating issues of accuracy and stability in algorithm design.
Technical obstacles to be addressed are the accurate inclusion of
lubrication forces when filaments approach each other, and the
development and application of fast summation strategies for
evalluating filament-filament interactions. The investigators will
also develop especially efficient methods for the special case of
rigid filaments. They will apply these methods to a set of current
theoretical issues, such as the development of normal stress
differences in flexible fiber suspensions, the effect on fluid mixing
of storing and releasing elastic stress in the fluidic microstructure,
and the large-scale dynamics of rod-like self-locomoting elements (as
arises in modeling bacterial baths)

The dynamics of microscopic flexible fibers immersed in a fluid are
essential to understanding many current problems arising in biology,
engineering, and physics. Examples range from manufacturing processes
in the pulp and paper industries to new proposed methods for mixing
fluids in small devices to the locomotion of micro-organisms. These
are all complicated systems whose dynamics are not well understood, in
part because the large-scale dynamics of the flow can depend on the
detailed nonlinear dynamics of the microscopic fibers. To help
increase our understanding of such problems, the investigators are
developing efficient and accurate methods for numerically simulating
the dynamics of such systems with many interacting fibers. They will
apply these methods to a set of current applications, drawn from the
basic physics of fluids, engineering, and biology.

Liquid crystal elastomers (LCEs) are rubbers whose
constituent molecules are orientationally ordered, with their
salient feature being a strong coupling between the orientational
order and mechanical strain. A characteristic feature of LCEs is
that relatively small external effects, such as changes in
temperature or onset of illumination, can produce huge and rapid
deformations. LCEs will likely assume real technological
importance due of their softness and their ready responsiveness
to applied fields, yielding applications in microfluidic pumping
and switching, and helping to answer basic questions in
locomotion. By extending the theory of rubber networks, the
investigators develop and explore continuum descriptions of these
materials, and study how LCEs behave in the bulk and in
interaction with an external fluid, and begin to develop
simulational methods for these systems. Parallel to the
theoretical study is an experimental program that involves the
applications of LCEs, such as to locomotion, but also to new
materials synthesis.

Liquid crystal elastomers (LCEs) are active flexible
materials whose constituent molecules can be reoriented or
disordered by applying electric or temperature fields. A
consequence of this is that relatively small external effects,
say in temperature changes or an onset of illumination, can
produce huge and rapid deformations of the material. The
investigators have already demonstrated that LCEs can have
fascinating dynamics when interacting with a fluidic environment,
such as the observed "swimming" of floating LCE samples away from
an illuminated region. These materials may be of technological
importance due of their softness and responsiveness, suggesting
applications in microfluidic pumping and switching, and helping
to answer basic questions in locomotion. To fully exploit these
materials the development of soundly based mathematical models is
crucial. The investigators develop mathematical descriptions of
these materials, and seek to understand the ways in which LCEs
interact with applied fields and with their environment.
Parallel to the theoretical studies is an experimental program
that involves the applications of LCEs, such as to locomotion,
but also to new materials synthesis.

Problems in biological fluid dynamics typically involve the interaction of an elastic structure with a surrounding fluid. Mucus transport by cilia in the respiratory tract, sperm penetration of the oocyte in fertilization, and peristaltic contractions of the oviduct are examples of such interactions. Many biological fluids are actually complex; that is they are not liquids or mixtures of a simple molecular structure that yields Newtonian responses, but instead have complicated non-Newtonian mechanical responses that arise, usually, because they have suspended microstructure. While much progress has been made in the development of mathematical models and numerical methods for fluid-structure interactions in a Newtonian fluid, much work needs to be done in the case of complex fluids. This focused research group will use a combination of analytical, computational and experimental tools to investigate the dynamics of elastic structures coupled to a complex fluid. Accurate and robust numerical methods for viscoelastic fluids coupled to moving and flexible boundaries will be developed that build upon classical immersed boundary methods and particle methods previously designed for Newtonian fluids. Continuum descriptions of the viscoelastic fluid will be implemented, as well as models that track discrete viscoelastic microstructure of the fluid. While the methods developed will be widely applicable, the team will focus upon the biofluidmechanics of reproduction, nematode motility in microfluidic chambers, as well as mucus-ciliary transport. Computational models will be coordinated with physical and biological experiments performed at the Applied Mathematics Lab at the Courant Institute.

Mathematics has had a huge impact on engineering and the physical sciences through its development of theoretical analyses and numerical methods for Newtonian fluid flows. The dynamics of complex fluids is emerging as another such opportunity, and is one which draws some of its richest problems from new areas in biophysics and engineering, medicine and reproductive health, and from core biology. The integration of mathematical and computational analysis into biological science presents educational challenges and great opportunities. This research project embraces these challenges, and is based upon collaborations of investigators at four institutions - Tulane University, New York University, Washington State University and the University of California, Los Angeles. A central component of this project is the training of graduate students and postdoctoral researchers. This FRG project will sponsor two summer programs, where the postdoctoral researchers and graduate students will spend six weeks at the Applied Mathematics Lab at Courant Institute. This will provide opportunities for all the students and postdocs involved in the project to work together side by side, develop a comprehensive understanding of the various aspects of the research, and experience and participate in the life of a working fluids lab.

The proposal utilizes an interdisciplinary approach to study the locomotion of C. elegans and their sensory response to environmental variations. C. elegans is one of the mostly studied model animals in biology due to its genetic tractability, sequenced genome, simple anatomy and body transparency. It is also a superb system to study mobility and sensing. This project will use C. elegans as a simple model system of living organisms to obtain critical physical information for understanding the interplay between sensing, locomotion and environment, incorporate this information into theoretical and computational models of undulatory locomotion.

This is a collaborative research project between a mechanical engineer at Washington University and a mathematical at the New York University.

This research is expected to impact on smart sensing and actuation technology, and the results will serve as building blocks for development of smart devices that can lead to robust design of adaptive systems and structures.

This award will make possible the purchase of a system of Particle Imaging Velocity (PIV), a universal research microscope, a rheometer and a few smaller equipments. With these instrumentations, the investigators will study a number of fluid problems that involve unsteady fluid flows interacting with mobile boundaries. In particular, it is planned to study the free flight of a rigid wing that is flapped at prescribed wave forms. The PIs will address questions related to the generation of thrust at early stages as the wing initiates a unidirectional flight. They will also study the effects of a flapping wing that is able to pitch during its flight, and compare its performance to a non-pitching wing, as well as the instability associated with flapping flags and the mechanism by which forced flags produce different types of wake structures. This experiment will address the question of the connections and differences between a flapping flag and a swimming fish. Moreover, it is well known that fluid pumping and animal locomotion share many common aspects, and can be studied using similar theoretical treatments. The planed study will investigate the transport of fluid using anisotropic geometry (ratchets) and the swimming of a model organism (C. elegans) in viscous fluids. The studies will be extended to complex fluids, since nonlinear responses take place in these systems even at low Reynolds numbers. The requested instrumentations will realize a fundamental improvement at the Applied Mathematics Laboratory (AML), which will allow the investigation of dynamical boundary problems in moving fluids with added precision and flexibility. The research projects will involve scientists at all levels, ranging from faculty members to motivated undergraduate and high-school students.

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).

Biologically active suspensions, of which a bath of swimming bacteria is a paradigmatic example, are fluid systems whose microstructure is alive and motile. As the system's "active particles" propel themselves through the surrounding fluid, they produce disturbance flows that communicate their motions to other swimmers, thereby altering their swimming direction and speed. This reciprocal interaction can result in correlated, large-scale, and complex fluid flows that move on length- and time-scales much larger than those of any single swimmer. These swimmer-driven flows have important implications for the evolution and survival of micro-organismal colonies, as they impact nutrient delivery through both particle transport and fluid mixing, and may also play a role in other important phenomena such as quorum sensing and biofilm formation. They are also fundamental examples of non-equilibrium pattern-forming systems. In this project, we propose to further deepen our understanding of biologically active suspensions using a combination of analytical models and numerical simulations. The research will focus on the modeling and analysis of the coherent structures that arise in these systems and on their relation to fluid mixing. Specifically the effect of boundaries and boundary conditions, confinement, and system scale will be examined. New multiscale approaches allowing hundreds of thousands of interacting swimmers to be simulated will also be developed, thus approaching biological realism.

As a result of this study, an improved theoretical understanding of active suspensions will be achieved and will reveal the core biophysical mechanisms underlying nutrient transport and mixing in colonies of motile microorganisms. It may also shed light on the evolution of locomotory strategies, particularly for microorganisms that live and thrive cooperatively, as in biofilms. The broader impacts of this research lie in the importance of active suspensions to several key areas of science, including biology, human health and medicine, soft-condensed matter physics, and engineering. An understanding of active suspensions and what drives (or stops) their large-scale mixing could lead to new ways of controlling infection. It provides to physics a well-characterized example of nonequilibrium pattern formation arising in biology, and in engineering this understanding could lead to new devices that exploit biological materials for tasks such as mixing and pumping. This project's impact also lies in the development of new and important areas of inquiry for applied and computational mathematics, and in its adding to the theoretical and computational tool-kit that applied mathematicians and theoretical engineers can bring to problems in biological and complex fluid dynamics.

The mitotic spindle forms during cell division and separates chromosomes into the daughter cells. It is required for normal eukaryotic cell division. In most cells, the division plane position and orientation is controlled by spindle position and orientation. However, the force mechanisms underlying spindle positioning are ill-understood. Two alternative models have been proposed. One invokes microtubule interactions with the cell cortex, and the other with the cell cytoplasm. The goal is to discover which model (if not both) is correct by using modeling, simulation, and experiments in C. elegans early embryos. The project team has skills in biophysical theory, experiment, mathematical modeling, and simulation. An essential difference between the two models is whether microtubules interact actively or passively with the cytoplasm, but given the system's complexity it is difficult to discriminate with experiment alone. We will use modeling and simulation to predict cytoplasmic flows associated with each model, and their combinations, and compare these to experimental measurements of actual flows. Detailed hydrodynamic interactions have not been previously accounted for in modeling spindle dynamics, and requires novel methods for efficiently and accurately capturing spindle microtubules interacting with each other, the cytoplasmic fluid, and the cell periphery. We will compare the predicted dynamics to new experimental measurements that simultaneously capture spindle structure and dynamics, and cytoplasmic motions. Comparisons will be made between predicted and observed responses under physical, molecular, and genetic perturbations. Intellectual Merit: The proposed work will bring a new approach to modeling mitotic spindle dynamics and positioning. The integrated experimental and theoretical approach will enable new insights into the mechanisms of positioning and asymmetric cell division. The project will contribute to the broader efforts to understand the mitotic spindle and cell division, a long-standing fundamental problem in cell biology. This work will expand technical knowledge in cellular biology, biophysics, experimental technique, statistical physics, applied math, fluid dynamics, partial differential equations, and numerical analysis.

Soft active materials are collections of particles, cells, or molecules that are capable of converting chemical energy from their environment into motion and mechanical stresses. Examples include swimming microorganisms, cellular extracts, biological polymers, and molecular motors, as well as a wealth of synthetic particles designed to mimic biological systems. These active systems, which have generated considerable excitement over the last decade in many disciplines from engineering to physics to applied mathematics, evince behaviors that are fundamentally different from traditional passive materials, and their understanding is just beginning to illuminate long-standing problems in biology and to suggest new engineering devices. This research project aims to use experiments, modeling, and simulations, to further enhance understanding of a variety of active materials. The project will also involve training through research involvement of postdoctoral researchers, graduate students, and undergraduates.

The aim of this project is to use a combination of modeling, mathematical analysis, numerical simulations, and experiments to explore the dynamics of archetypal active fluids as their microstructural components interact with obstacles, walls, and each other. Computational and coarse-grained models will explore the interaction of microswimmers, individually and collectively, with boundaries and obstacles. Microfluidic environments will be fabricated to explore how active particle transport is affected and controlled by boundaries and obstacles, and tools of shape optimization will be used to guide the design. Specialized particles will be fabricated to elucidate different aspects of active matter. New types of active matter will be explored, both by considering modifications in particle-scale activity and system-scale confinement. These investigations will include detailed and coarse-grained computational models of recently synthesized active fluids in which immersed microtubules interact through motor-protein cross-linking and pulling, as well as a new active matter system in which particle activity couples to interfacial forces to drive large-scale flows.

This award supports a research collaboration on mathematical and numerical modeling and analysis of failure in soft materials. This research project concerns the derivation and numerical implementation of a mathematical theory capable of describing, explaining, and predicting the initiation and propagation of fracture in soft organic solids---namely, solids made up of networks of long carbon-based macromolecules such as elastomers, gels, and biological tissues---when subjected to arbitrarily large mechanical forces. Soft organic solids are known to fracture in a very different manner than standard hard solids (such as metals and ceramics). The defining difference is that internal fracture in soft organic solids initiates through the sudden growth of inherent defects into large enclosed cavities/cracks (a phenomenon popularly referred to as cavitation). With the ever-increasing use of soft materials in new technologies, a fundamental and quantitative understanding of when and how organic solids fracture is of utmost importance for their advancement. Likewise, such a fundamental and quantitative understanding is critical in advancing medical treatments involving soft biological tissues, such as shock-wave lithotripsy, or treatments dealing with aneurysms.

This project centers on a novel variational theory of fracture for finitely deformable solids that is consistent with the principle of conservation of mass (a highly non-trivial feature that has been overlooked in the literature by related formulations) and wherein the newly created surfaces (by fracture) are not restricted to be hypersurfaces (as in classical brittle fracture) but can also be the boundaries of N-dimensional cavities, N being the spatial dimension. The main objectives of the project are: (1) to develop a formulation in terms of variational evolutions for the initiation and propagation of fracture in soft organic solids under arbitrarily large quasi-static deformations, and (2) to implement this formulation numerically and confront its predictions with emerging experimental evidence of high spatio-temporal resolution. Objective (1) entails rigorous existence results, while objective (2) entails the construction of appropriate approximate functionals (of the phase-field type) and their stable and convergent numerical implementation in the non-convex context of finite deformations with constraints (in particular, incompressibility).

This project, developing a distributed instrument to physically integrate seamlessly the physical with the virtual, aims to create a unique experiential supercomputer, an immersive, collaborative, virtual/physical research environment with unparalleled tools for intellectual and creative output, a Holodeck that scientifically exceeds Star Trek science fiction. The work should advance the next-generation experiences in human interaction and deep integration of virtual and physical settings, creating rich actualizing environments to support research and discovery of new paradigms. The flexible, modular, reconfigurable infrastructure will connect researchers, research, and educational facilities across the university, the NYU Global Network University (GNU), and external researchers, communities, and industry partners worldwide. The instrument will enable exploration of a myriad of research questions involving virtual environments, telepresence, collaborative engagement, and remote interaction and create a strong foundation for extended collaborations. The project integrates qualitative and quantitative assessment of affect and motivation, with foundations of learning science, motion science, acoustics, modeling and simulation, robotics and fabrication to improve research effectiveness and scalability to address real world challenges.

The work is accomplished by integrating 3-D printing to physically realize simulated forms, robots to allow virtual models to impact the physical world and interact with it, haptics to provide to human collaborators a sense of tactile feel of virtual objects, and physiological state monitors to try to get "inside" the human experience. This "experiential supercomputing" serves as a paradigm for human collaboration that translates to all disciplines spanning computer science, engineering, music, psychology, nursing, radiology, applied math, biology, and medicine. The effort transcends visualization to approach human collaboration in its totality and has the potential to transform our fundamental understanding of collaboration, learning, creativity, discovery, and innovation. The NYU Holodeck will be a well-integrated software/hardware instrument incorporating visual, audio, and physical components and novel technologies to enhance social interactions (human-human, human-agent, and human-robot). In its incorporation of rapid prototyping and fabrication tools, this unique instrument fosters creative capacity, and tight coupling of interactive visual, audio, and physical experience. Its research capabilities support comprehensive capture of behavioral, physiological, affective, and cognitive data, and visualization and analysis of the data in real time. Creating innovative environments that bridge simulation, cyber learning, scientific visualization, human-computer interaction, and applied physical science research; the effort enables new types of science where researchers from diverse disciplines can interact with theoretical models, real objects, robots, and agents, engendering insights not possible using 2D, 3D, or other currently available representations.

Active cellular matter is the basis of novel synthetic active fluids made of mixtures of suspended cytoskeletal filaments and molecular motors. By consuming chemical fuel, the molecular motors (e.g., kinesins) can bind to and create actively moving crosslinks between the biofilaments (e.g., microtubules) to drive their relative motion, which leads to large-scale collective motions in the filament/motor mixture through hydrodynamic coupling. Synthetic active suspensions made of small numbers of components reveal how higher-order aspects of assembly and organization are built in living cells. These systems also present new challenges to our understanding, design, and analysis of materials, and have the potential to provide valuable new technologies such as autonomously moving and self-healing materials.

In this work, the investigators study active cellular matter composed of microtubules and molecular motors through multiscale methods, and tightly coupled modeling, analysis, and simulation. The project aims to understand the fundamental interactions underlying stress generation within bundles of rigid/flexible biofilaments that undergo dynamic instability, as well as the nonlinear dynamics and hierarchical pattern formation in large-scale collective motions. The project will also predict key material properties including its coherent structures, local heterogeneity, time- and length-scales, and material rheology. To resolve the physics at different length- and time-scales, several methods will be developed and integrated: (1) microtubule-motor interactions will be simulated using a kinetic Monte Carlo method; (2) the hydrodynamic interactions between objects of various shapes will be modeled using a nonlocal slender body/boundary integral method, together with fast summation methods; (3) a pseudo-spectral method will be implemented to simulate the collective motion through a continuous active liquid-crystal type model.

Nontechnical Abstract:
Biological systems exhibit remarkable behaviors, including the ability to heal, reproduce, and be self-motile. Conventional synthetic materials do not display such properties because they are composed of inanimate molecules. In contrast, biological systems consist of active, energy transducing molecules which continuously push and pull on each other, producing active stresses. These active stresses make biological systems examples of active matter, and are ultimately are responsible for many of their unusual behaviors. Creating artificial active matter opens up a new route towards constructing materials with lifelike functionalities. However, a significant obstacle to realizing this possibility is an absence of understanding of how active stresses are produced: given specific elemental building blocks, there are not currently tools to either measure or theoretically predict the magnitude, type, or even the sign of the active stresses. The project will elucidate the foundational principles of active stress generation using a synergistic combination of experiments, simulations, and theory. The work will result in the creation of new experimental tools for measuring active stresses, new synthesis procedures for creating active materials, and new multi-scale modeling techniques for studying active matter. An integrated outreach program will bring the excitement of active matter to K-12 education, undergraduates, and graduates by combining interactive demonstrations, advanced interdisciplinary training, and intensive summer courses.

Technical Abstract:
The research focuses on studying assemblages of microtubules and kinesin-14 molecular motors. The work addresses three fundamental challenges in understanding active stresses generated by such active materials. First is the development of tools to measure active stresses at different length scales using optical tweezers, fluid flow measurements, microfluidics, and 3D printing, in combination with theory and simulations. Second, a novel system will be created in which active stress generation will be modulated by directly affixing kinesin-14 to microtubules in predetermined patterns. Theory and simulations will be used to guide which patterns to create, and conversely, measuring the resulting active stress generation in these designed materials will provide a stringent test of theory and simulations. Third, a multi-scale modeling framework will be developed and tested. These will be subsequently related to each other through a combination of analytical calculations and simulations. The resulting models will be made with continual feedback from experiments. Taken together, this work will establish new paradigms to study, understand, and engineer active stresses in active materials.

This DMR grant supports research to understand the assemblages of microtubules and kinesin-14 molecular motors with funding from the Condensed Matter Physics (CMP) and Biomaterials (BMAT) Programs in the Division of Materials Research of the Mathematical and Physical Sciences Directorate.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.