http://mmnorton.com/analyses daily 0.75 2015-04-22 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1429745921033-MZP28YASRK79AZ0WDHBA/image-asset.jpeg Analyses - Induced Charge Concentration Polarization around Nano-Sphere When an electrically neutral, dielectric sphere is placed in a symmetric binary electrolyte, and subjected to an electric field, polarization of the particle and the electrolyte surrounding it results. The polarization of the electrolyte takes place within a relatively thin layer around the particle known as the electric double layer (or Debye layer). For micron-scale colloids, this layer is thin compared to the radius of the particle; the disparity in length scales can be used to find tractable analytical solutions for the electric potential and charge distributions around the particle. For nano-particles, this assumption is not valid. Instead, I assume that the electric field is weak and use it as a regular perturbation parameter. At first order in E*, I find the electric potential and charge distribution. At second order, I find the streamlines for the electro-osmotically induced flow and spatial distribution of total charge carriers (pictured). The electric field is directed from south to north; the contours show that the total number of charge carriers or "excess electrolyte" is greater than the bulk around the equator of the particles, and less than the bulk at the poles. https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1429745921033-MZP28YASRK79AZ0WDHBA/image-asset.jpeg Analyses - Induced Charge Concentration Polarization around Nano-Sphere When an electrically neutral, dielectric sphere is placed in a symmetric binary electrolyte, and subjected to an electric field, polarization of the particle and the electrolyte surrounding it results. The polarization of the electrolyte takes place within a relatively thin layer around the particle known as the electric double layer (or Debye layer). For micron-scale colloids, this layer is thin compared to the radius of the particle; the disparity in length scales can be used to find tractable analytical solutions for the electric potential and charge distributions around the particle. For nano-particles, this assumption is not valid. Instead, I assume that the electric field is weak and use it as a regular perturbation parameter. At first order in E*, I find the electric potential and charge distribution. At second order, I find the streamlines for the electro-osmotically induced flow and spatial distribution of total charge carriers (pictured). The electric field is directed from south to north; the contours show that the total number of charge carriers or "excess electrolyte" is greater than the bulk around the equator of the particles, and less than the bulk at the poles. http://mmnorton.com/hobby-horses daily 0.75 2023-04-07 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1401773425820-VNFSJUYB67LW3IRPHSHR/20120811_170153.jpg Hobby Horses - MIG welding practice, Boxes https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1401772708756-PO0Y9J7I0IPSGQZXN7BG/20130322_181150.jpg Hobby Horses - AV10 Engine Testing Stand http://mmnorton.com/blog daily 0.75 2014-08-13 http://mmnorton.com/mini-projects daily 0.75 2015-09-23 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1427166938267-1YF16B2AEU8VZG7A6VO5/1500_10000_b_websitegif.gif Experiments - Visco-Capillary Instability The video (played in real time) shows a mineral oil jet (black) passing over a solid inner core (a single optical fiber obscured by the oil) surrounded by a background flow of glycerol. The image is roughly 1mm in height. The high viscosity of the fluids ensures that the Reynolds number is low despite the somewhat large size and serendipitously keeps the oscillation frequency low enough to observe at 30 fps. These particular oscillations appear spontaneously and are being observed at a spatial station a few centimeters downstream from the nozzle that introduces the heavy mineral oil into the glycerol stream. The oscillations grow in amplitude and far downstream result in a train of droplets that appear to be nearly unduloidal in shape. Click to download a video of the device generating this flow at low magnification. https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1427166938267-1YF16B2AEU8VZG7A6VO5/1500_10000_b_websitegif.gif Experiments - Visco-Capillary Instability The video (played in real time) shows a mineral oil jet (black) passing over a solid inner core (a single optical fiber obscured by the oil) surrounded by a background flow of glycerol. The image is roughly 1mm in height. The high viscosity of the fluids ensures that the Reynolds number is low despite the somewhat large size and serendipitously keeps the oscillation frequency low enough to observe at 30 fps. These particular oscillations appear spontaneously and are being observed at a spatial station a few centimeters downstream from the nozzle that introduces the heavy mineral oil into the glycerol stream. The oscillations grow in amplitude and far downstream result in a train of droplets that appear to be nearly unduloidal in shape. Click to download a video of the device generating this flow at low magnification. https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1442987699539-FZMV8G0UMKACL6SSFNAY/CeleganDrop.png Experiments - C. elegans nematode in a water drop What it is: A still from this video of a C. elegans nematode encapsulated in a water drop, surrounded by oil, floating atop a water bath. The specimen was inserted into the droplet using hydrodynamic flow focusing. Originally, the intent was to isolate specimens for high through-put screening; surfactant at the oil-water interface renders the individual droplets resistance to coalescing. What it could be: It turns out that the system may be interesting for more fundamental reasons. Colloids and emulsions can be used as model systems to study crystallization, glasses, and the dynamics of defects. Here is an example of droplets (empty) shifting around, trying to form a perfect lattice (again, these are water drops, surrounded by oil, floating atop water). In this case, capillary action (the "cheerio" effect) provides an attractive potential. It would be interesting to dope such an emulsion with some active nematode laden drops to see how the lattice responds to local, periodic, and anisotropic distortions. While applying bulk forces to such systems has been done in the past, such a local probe would be very interesting to explore.   https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1429544632336-F99V6VF44XASEMGUJTCX/RIT_FuelCellDesign_Norton.png Experiments - "Transparent" Hydrogen Fuel Cell Assembly This is a snapshot of the fuel cell setup I helped design in conjunction with General Motors scientists as a research intern in Dr. Satish Kandlikar's lab at RIT in 2007. The main design goal was to fabricate a fully functional fuel cell that would feature transparent flow channels to allow the observation of water transport during operation. Water management is crucial to proper FC operation: too little and the PEM ceases to function; too much and flooding prevents fresh hydrogen and oxygen from being introduced. As of 2014, the cell was still in operation. (1) End Plate, (2) Die Springs, (3) Viewing Window, (4) Metal Case, (5) Air/Hydrogen In/Out, (6) Heating/Cooling Water In/Out, (7) Flow Field Lexan Plates, (8) Cathode & Anode Channels. http://mmnorton.com/illustrations daily 0.75 2018-12-20 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1427167520618-HD0YHHR97WE41ECSMOWB/imagesystem3.jpg Illustrations - Image System for a Slender Body Inside a Spherical Cavity Schematic for extending Johnson’s work on the fluid dynamics of slender bodies at low Reynolds numbers to slender bodies within spherical cavities using the image system of Maul and Kim. https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1427167520618-HD0YHHR97WE41ECSMOWB/imagesystem3.jpg Illustrations - Image System for a Slender Body Inside a Spherical Cavity Schematic for extending Johnson’s work on the fluid dynamics of slender bodies at low Reynolds numbers to slender bodies within spherical cavities using the image system of Maul and Kim. https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1429546009154-2HBJKXQSTI6X6I0URW2T/electrodegrowth.png Illustrations - Electrodeposition in an Electron-Microscopy Liquid Cell Artistic rendition of electro-deposited copper growing in a highly confined (200 nm) channel bound by silicon nitride membranes. The illustration depicts the transition from full 3D growth at early times to a 2D front at later times. Understanding this transition time is important for interpreting experimental results. I did the figure to help out a cohort Nicholas Schneider who is studying several phenomena related to electro-deposition. http://mmnorton.com/hands-on daily 0.75 2023-04-07 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1401773355287-I6V2PPBVCKZYZSW7DHGO/IMG_20140503_004227.jpg shop - Pyramid BBQ and Firepit I really enjoy playing around with basic geometric forms. This is an in-progress shot of a BBQ and firepit made out of sheet metal. When not in use, it casts an ominous shadow on my yard, which I enjoy. The weak link in this project was cutting out the forms and holding them in place. I was using an angle grinder with a cutting disk and even my best efforts left enough gaps to make TIG welding impractical. Despite the difficulty, I got the sculpture bug from this project. Realizing how important it is to start out with good cuts is what motivated me to make the CNC Plasma Cutter. https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1401773355287-I6V2PPBVCKZYZSW7DHGO/IMG_20140503_004227.jpg shop - Pyramid BBQ and Firepit I really enjoy playing around with basic geometric forms. This is an in-progress shot of a BBQ and firepit made out of sheet metal. When not in use, it casts an ominous shadow on my yard, which I enjoy. The weak link in this project was cutting out the forms and holding them in place. I was using an angle grinder with a cutting disk and even my best efforts left enough gaps to make TIG welding impractical. Despite the difficulty, I got the sculpture bug from this project. Realizing how important it is to start out with good cuts is what motivated me to make the CNC Plasma Cutter. https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616891743640-QQNAUPJD6V7OWG3MDMQ8/IMG_7394_20210327_161857.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616892158960-FJ7NM006RBL1CT0M7HA9/IMG_7387_20210327_161857.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616895069828-7WAHVWC59IDB85PDA19E/tripotrendersketch.png shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616892158061-KFS8RNBCE4EJNWMKE6DE/Attach55587_20210320_171142.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616899469751-VGP7ZGT2JG3RB0JJVY77/20210320_175137.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1514750321583-0XY7VL4ZACI4HJLUQ9YG/20171015_223230.jpg shop - CNC Plasma Cutter and Downdraft Table I fabricated a 5'x4' CNC Plasma Cutter and downdraft table. I am using the cutter to make planar sheet metal forms that I fold into 3D objects and sculptures. Since I don't have easy access to a full machine shop, I tried to use off the shelf components as much as possible for the keep components. Linear motion parts (bearing blocks and gantry supports) came from CNC Router Parts. Z-axis assembly utilizes 80/20 compatible aluminum plates and a few custom welded steel brackets. Since lateral forces are minimal for plasma cutting, the X-Y motion is belt driven (GT2 9mm width belt). The downdraft table is my own design built from steel channel, 2''x3'' tube, removable 1/16'' steel plate to contain dust and sparks, and a removable steel slat cutting surface. Ventilation provided by a 16'' 4/5 HP utililty blower. https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616894014487-63ARVU8GU5J025VKVHUC/IMG_0150+%281%29.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1401772842327-D3ATCF2C1VW7PXQ4OZ07/20130406_154425.jpg shop - Ready for welding https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1401772975593-RFOSUGSDM20JUZ92WR45/20140308_235500.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1514750169020-8VNKSU9K14GU8JC8DATW/20171015_223230.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616892229843-DYGCNVXJT4SMT9ZS05U2/20210327_202703.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616893187976-PC1IGPAVCKNS80G53BVD/20160724_154255.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616894193130-S6DYBG6V8SKI0C57SL9O/Attach54617_20210116_124948.jpg shop https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1616894113579-9YY8HGUXQK9UIX0OQTCM/Attach54963_20210209_165906.jpg shop http://mmnorton.com/brandeis-research daily 0.75 2018-02-12 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1518393535544-KAUPAGO6CC7F13I79FBZ/activenematic_turb.png Brandeis Research - Active testing test ing   https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1518393535544-KAUPAGO6CC7F13I79FBZ/activenematic_turb.png Brandeis Research - Active testing test ing   https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1518393562699-UDA1DZ74MIY37DIXO8LT/CPG.png Brandeis Research - Neuro-mimetic Reaction-Diffusion Systems testing http://mmnorton.com/projects daily 0.75 2015-03-18 http://mmnorton.com/publications daily 0.75 2025-04-15 http://mmnorton.com/new-page daily 0.75 2020-01-31 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1519705961474-K1INABOJQTSFGKRR0K28/activenematic_turb.png Active Fluids Active fluids transduce energy from the environment into useful work at the molecular scale. In contrast, classical fluids are only driven at the macro-scale by boundaries and pressure gradients. The distributed and embedded nature of the force-injection of these fluids gives rise to striking phenomena such as self-circulation and turbulence even at vanishing Reynolds number. One class of active fluids are those composed of elongated active units, such as ellipsoidal swimmers or microtubules. At high density, these systems spontaneously create a nematic phase with orientational order. Like passive liquid crystals found in display technology, these systems can possess defects and topology-dependent configurations. The hydrodynamic flows created by molecular activity, however, compete with boundary-imposed ordering. I am currently using continuum-level models to understand the impact of boundary conditions on the flow and defect dynamics. I am also working with experimentalists to develop image processing techniques to quantify observed dynamics. (Top) Finite element simulation results showing the nematic director field (black lines) circulation of two +1/2 defects (magenta arrows). Boundary conditions are parallel anchoring for the director field and no-slip for the flow field. Points from four initial quadrants are labeled in yellow, red, green and cyan to convey the complex deformations undergone by material points. (Left) Finite element results showing the director field (black lines), -1/2 defects (blue), +1/2 defects (magenta arrows). Perpendicular anchoring is imposed through an energy-penalty boundary condition; however, the flow "combs" over the director in many locations. The high defect density occurs because the active stress is high. From Insensitivity of active nematic liquid crystal dynamics to topological constraints, PRE. https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1519705670058-QU8W6U2RWPPD3XUILD2K/CSmixing.png Active Fluids http://mmnorton.com/about daily 0.75 2024-11-07 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/213af1d4-b0e6-49f0-9ac7-8ef0209c7e26/011422_D0011_mmn_circle.png About http://mmnorton.com/oscillator-networks daily 0.75 2020-01-31 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1519496577929-36OI2SFJODWNVQLB0EFG/CPG.png Oscillator Networks - Oscillator Networks from Reaction-Diffusion Media PI: Seth Fraden Inspired by the autonomous nervous system, we seek to develop synthetic systems that create spatio-temporal patterns from oscillatory sub-units. In Engineering reaction–diffusion networks with properties of neural tissue we demonstrated that the oscillation patterns of the Belousov-Zhabotinsky reaction could sculpted into a functional network using microfluidics. Such a material could lay the foundation for the control layer in soft-robotics. I am currently studying the relationship between network topology and the multiplicity of dynamic steady states that oscillator networks can exhibit. (Right) Dual column central pattern generator modeled after the lamprey eel spine. The network features columns that propagate signals through excitatory interactions. The columns themselves are linked through inhibitory coupling, this drives each of the columns out of phase. The designed stable attractor of the system is therefore left-right-left-right firing pattern. (First panel) Finite element simulation of the BZ reaction. The BZ media is confined to the square wells and channels, the surrounding media is selectively permeable to the inhibitor, Bromine, whose concentration field is shown. Snapshots are spaced one oscillation period apart to show the beginning of the shift towards anti-phase synchrony. (Second Panel) Microscopy image of the completed microfluidic network, the chemical state of the well is indicated by a color change (appears bright in the image). http://mmnorton.com/code daily 0.75 2022-12-17 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1610827540987-X84CNRJ388JXHY1A520L/oc_traj_schm.png Code https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1610827577054-PK602I7HJ2DUI4RX5NIX/defectindex_plushalf.png Code http://mmnorton.com/research-2-1 daily 1.0 2025-05-13 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/52ecb653-9948-4549-8306-9eca12296294/frames_cates_20240108_g_15_free-1_wb-1_contrast.gif Research - Research Overview My goal is to develop strategies for steering and designing living systems. Biology effortlessly self-organizes through entwined chemomechanical and reaction-diffusion processes, enabling multi-time and lengthscale feats such as sensing environmental queues, cell division, and morphogenesis. Nonlinear and interdependent, unraveling the biological processes enabling these dynamics is a cross-disciplinary endeavor. To tackle these challenges, I employ computational tools and concepts from non-equilibrium soft-condensed matter physics, fluid dynamics, nonlinear dynamics, and control theory. Driven by experimental collaborations, I explore these themes through several physical systems, including: 1) light-activated microtubule-kinesin nematics (Fraden, Dogic, Hagan, and Grover), 2) actin polymerization-driven beads (Duclos and Hagan), 3) reconstituted minD/E (Duclos and Touboul), and 4) Belousov-Zhabotinsky oscillators (Fraden). Funding: 1. Department of Energy, Basic Energy Sciences, Biomolecular Materials DE-SC0022280 (role: Co-I, PI Grover at UN-L) 2. Brandeis University NSF MRSEC DMR-2011846 https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1730942019555-MP1D87ISDR951PJG39RW/3d_20241024_b_smaller_b_wb.gif Research - minD/E minD/E https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1730942031870-4RR7VM54J68W9JSUCCLB/Reset+2vd.avi+%281%29.gif Research https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1731000810593-AXQ20BMQILDRRAGRHY9V/defectlattice2.png Research https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1730942095341-HV27JF7ABI8ZMJ7B247Q/movieS2_case2_bw.gif Research https://images.squarespace-cdn.com/content/v1/5332077ce4b02ebf3fbb6d02/1730942033214-KO0VYOKK8ZEC1X89W6FE/optocontrol_wb.gif Research