Academic Positions

  • Present 2016

    Associate Professor

    University at Buffalo,
    Department of Mechanical and Aerospace Engineering

  • 2016 2010

    Assistant Professor

    University at Buffalo,
    Department of Mechanical and Aerospace Engineering

  • 2010 2007

    NSF Research and Teaching Grant Postdoctoral Fellow

    Northwestern University,
    Department of Engineering Sciences and Applied Mathematics

Education & Training

  • Ph.D. 2007

    Ph.D. in Mechanical Engineering

    University of Michigan

  • M.S.2007

    Master of Science in Mathematics

    University of Michigan

  • B.S.2002

    Bachelor of Science in Mechanical Engineering

    Michigan Technological University

Honors, Awards and Grants

  • 2013-2018
    NSF Career Award: Electrohydrodynamics of Vesicles
    image
    The objective of this award, co-funded by the Biomaterials Program in Division of Materials Research, is to perform in-silico and in-vitro investigations of single and multicomponent vesicles in fluid flow and during exposure to electric fields. Vesicles exposed to the combined effects of fluid flow and electric fields have shown a wide and varied set of behaviors. Exposure to electric fields have induced vesicle shapes not normally accessible. Weak electric fields have induced lipid flow patterns in the membranes of multicomponent vesicles. As the electric field strength is increased pores begin to form in the vesicle membrane. This allows foreign substance to either enter or leave the vesicle. Vesicles exposed to strong electric fields have been shown to burst. It is unknown how exposure to combined fluid and electric effects will influence vesicle behavior. The proposed work will answer the following specific biological questions: 1) How does the combined effects of fluid flow and electric fields influence the dynamics of vesicles and lipids in the vesicle membranes? 2) Under what conditions will electroporation occur and what is the lifespan of these pores?
  • 2007-2010
    NSF Research and Teaching Grant Postdoctoral Fellow
  • 2006
    Pan-American Advanced Studies Institute Fellow

Research Summary

Many engineering systems involve moving interfaces. Examples include the self-assembly of molecules on surfaces due to electric fields and the dynamics of lipid bilayer vesicles.

I am interested in using advanced computational techniques to provide insight into the physics of such systems. These computational techniques couple multiple physics, such as those seen in multiphase fluid flow, into a coherent scheme which allows for the determination of the important parameters needed to obtain the desired behavior.

Interests

  • Level-Set Methods
  • Vesicles
  • Computational fluid dynamics
  • Magneto- and Electro-hydrodynamics
  • Material systems with Moving Interfaces
  • Numerical Methods
  • Directed Self-Assembly
  • High Performance Computing

Research Projects

  • image

    Electrohydrodynamics of Vesicles

    Understanding the electrohydrodynamics of vesicles has many possible applications, including directed drug delivery and lab-on-a-chip. In this project a three-dimensional model is developed using advanced level set and computational fluid dynamics techniques.

    In this project a three-dimensional numerical model of vesicle electrohydrodynamics in the presence of DC electric fields is developed. The vesicle membrane is modeled as a thin capacitive interface through the use of a new semi-implicit level set Jet scheme. The enclosed volume and surface area are conserved both locally and globally by a new Navier-Stokes projection method. The electric field calculations explicitly take into account the capacitive interface by an implicit Immersed Interface Method formulation, which calculates the electric potential field and the trans-membrane potential simultaneously. The results match well with previously published experimental, analytic and two-dimensional computational works.

  • image

    Electrohydrodynamics of Colloidal Particle/Droplet Systems

    Electric fields have been shown to direct the motion of immiscible droplets systems containing colloidal particles. This work will result in detailed knowledge of how the material parameters and the external electric field influence the structuring of the colloidal particles on the droplet surface.

    This research will result in a new unified numerical and experimental framework to understand and predict the behavior of mono-dispersed colloidal particles and liquid droplets in an immiscible liquid/liquid system during exposure to electric fields. This work will: 1) model the electrohydrodynamics of general three-dimensional colloidal particle/droplet systems, 2) experimentally investigate the dynamics of the system to provide validation of the numerical work and give insight into the influence of materials, 3) provide information about colloidal particle motion both in the fluids and on the droplet surface, and 4) systematically investigate the electrohydrodynamics of this system to provide a complete picture of the dynamics. The combined set of models and algorithms will result in a significant advancement of droplet based technologies such as directed drug delivery, micro-reactors, and micro-fluidics.

  • image

    Advanced Level Set Methods

    Level sets have become a very popular method to implicitly track the location of moving interfaces. In this project new level set methods to model moving interface systems, particularly those under stiff velocity fields, are being developed.

    Tracking a level set and it's derivatives lead to highly accurate descriptions of a moving interface. In this project the original advection schemes, which are only applicable to linear velocity fields, are extended to allow for the investigation of stiff, non-linear interface motion. This work will aid in the other modeling projects currently underway within the group.

Filter by type:

Sort by year:

Energy variation of soft matter interfaces

P.Gera and D. Salac
In Review Submitted to Communications in Mathematical Physics

Abstract

The variation of energies associated with soft matter interfaces where surface inhomogeneities are present. These energies include the total bending and splay energy, the variable surface tension energy, a coupling energy between the total curvature and an underlying surface concentration field, the energy due to an external field, and a phase segregation energy. When considering these energies the variation of material properties such a bending rigidity are taken into account, which results in more general variation expressions. These variations can be used to determine the equilibrium interface and concentration configuration or to determine the driving forces for non-equilibrium situations. While the focus of this work are energies associated with multicomponent vesicles, it can easily be extended to any soft matter interface.

Vesicles in magnetic fields

D. Salac
In Review Submitted to Soft Matter

Abstract

Liposome vesicles tend to align with an applied magnetic field. This is due to the directional magnetic susceptibility difference of the lipids which form the membrane of these vesicles. In this work a model of liposome vesicles exposed to magnetic field is presented. Starting from the base energy of a lipid membrane in a magnetic field, the force applied to the surrounding fluids is derived. This force is then used to investigate the dynamics of vesicle in the presence of magnetic fields.

The Cahn-Hilliard-Cook equation on curved surfaces in three-dimensional space

P. Gera and D. Salac
In Review Submitted to Physical Review E

Abstract

Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. One model which takes into account additive stochastic noise is the Cahn-Hilliard-Cook (CHC) model. Often, the surface on which phase segregation occurs is not a flat surface. With this motivation, we present a semi-implicit numerical algorithm to solve the fourth order parabolic stochastic partial differential equation on arbitrary curved surfaces. In addition to a description of the numerical method, the effect of Gaussian white noise in the CHC equation is also studied, to draw its significance during the phase segregation process.

Level set jet schemes for stiff advection equations: The SemiJet method

G. Velmurugan, E.M. Kolahdouz and D. Salac
Journal Paper Computer Methods in Applied Mechanics and Engineering, Volume 310, 1 October 2016, Pages 233-251

Abstract

Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems. The new method offers an improvement over the semi-implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy. Sample results demonstrate that accuracy is not sacrificed while strict time step restrictions can be avoided.

A general, mass-preserving Navier-Stokes projection method

D. Salac
Journal Paper Computer Physics Communications, Volume 204, July 2016, Pages 97-106

Abstract

The conservation of mass is a common issue with multiphase fluid simulations. In this work a novel projection method is presented which conserves mass both locally and globally. he fluid pressure is augmented with a time-varying component which accounts for any global mass change. The resulting system of equations is solved using an efficient Schur-complement method. Using the proposed method four numerical examples are performed: the evolution of a static bubble, the rise of a bubble, the breakup of a thin fluid thread, and the extension of a droplet in shear flow. The method is capable of conserving the mass even in situations with morphological changes such as droplet breakup.

Heuristic and Eulerian interface capturing approaches for shallow water type flow and application to granular flows

H. Aghakhani, K. Dalbey, D. Salac, A.K. Patra
Journal Paper Computer Methods in Applied Mechanics and Engineering, Volume 304, June 2016, Pages 243-264

Abstract

Determining the wet-dry boundary and avoiding the related spurious thin-layer problem when solving the depth-averaged shallow-water (SW) equations (or similar granular flow models) remains an outstanding challenge, though it has been the focus of much research effort. In this paper, we introduce the use of level set and phase field based methods to address this issue and related problems. We also propose new heuristic methods to address this problem. We implemented all of these methods in TITAN2D, which is a parallel adaptive mesh refinement toolkit designed for numerical simulation of granular flows. Results of the methods for flow over a simple inclined plane and Colima volcano are used to illustrate the methods. For the inclined plane, we compared the results with experimental data and for Colima volcano they are compared to field data. Our approaches successfully captured the interface of the flow and solved the accuracy and stability problems related to the thin layer problem in SW numerical solution. The comparison of results shows that although all of the methods can be used to address this problem, each of them has its own advantages/disadvantages and methods have to be chosen carefully for each problem.

Electrohydrodynamics of three-dimensional vesicles: A numerical approach

E.M. Kolahdouz and D. Salac
Journal Paper SIAM Journal on Scientific Computing, Volume 37, Issue 3, June 2015, Pages B473-B494

Abstract

A three-dimensional numerical model of vesicle electrohydrodynamics in the presence of DC electric fields is presented. The vesicle membrane is modeled as a thin capacitive interface through the use of a semi-implicit, gradient-augmented level set Jet scheme. The enclosed volume and surface area are conserved both locally and globally by a new Navier-Stokes projection method. The electric field calculations explicitly take into account the capacitive interface by an implicit Immersed Interface Method formulation, which calculates the electric potential field and the trans-membrane potential simultaneously. The results match well with previously published experimental, analytic and two-dimensional computational works.

Dynamics of three-dimensional vesicles in DC electric fields

E.M. Kolahdouz and D. Salac
Journal Paper Physical Review E, Volume 92, Issue 1, July 2015, Page 012302

Abstract

A numerical and systematic parameter study of three-dimensional vesicle electrohydrodynamics is presented to investigate the effects of different fluid and membrane properties. The dynamics of vesicles in the presence of DC electric fields is considered, both in the presence and absence of linear shear flow. For suspended vesicles it is shown that the conductivity ratio and viscosity ratio between the interior and exterior fluids, as well as the vesicle membrane capacitance, substantially affect the minimum electric field strength required to induce a full Prolate-Oblate-Prolate transition.In addition, there exists a critical electric field strength above which a vesicle will no longer tumble when exposed to linear shear flow.

A numerical model for the trans-membrane voltage of vesicles

E.M. Kolahdouz and D. Salac
Journal Paper Applied Mathematics Letters, Volume 39, Issue 1, January 2015, Pages 7-12

Abstract

The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second normal derivative, are derived. The trans-membrane potential is determined implicitly as part of the algorithm. The method is compared to an analytic solution based on spherical harmonics and verifies the second-order accuracy of the underlying discretization even in the presence of solution discontinuities. A sample result for an elliptic interface is also presented.

The effect of glass forming sugars on vesicle morphology and water distribution during drying

C.J. Vogl, M.J. Miksis, S.H. Davis, and D. Salac
Journal Paper Journal of the Royal Society Interface, Volume 99, Issue 11, October 2014, Page 20140646

Abstract

Cryopreservation requires that stored materials be kept at extremely low temperatures and uses cryoprotectants that are toxic to cells at high concentrations. Lyopreservation is a potential alternative where stored materials can remain at room temperatures. That storage process involves desiccating cells filled with special glass-forming sugars. However, current desiccation techniques fail to produce viable cells, and researchers suspect that incomplete vitrification of the cells is to blame. To explore this hypothesis, a cell is modelled as a lipid vesicle to monitor the water content and membrane deformation during desiccation. The vesicle is represented as a moving, bending-resistant, inextensible interface and is tracked by a level set method. The vesicle is placed in a fluid containing a spatially varying sugar concentration field. The glass-forming nature is modelled through a concentration-dependent diffusivity and viscosity. It is found that there are optimal regimes for the values of the osmotic flow parameter and of the concentration dependence of the diffusivity to limit water trapping in the vesicle. Furthermore, it is found that the concentration dependencies of the diffusivity and viscosity can have profound effects on membrane deformations, which may have significant implications for vesicle damage during the desiccation process.

A semi-implicit gradient augmented level set method

E.M. Kolahdouz and D. Salac
Journal Paper SIAM Journal of Scientific Computing, Volume 35, Issue 1, January 2013, Pages A231-A254

Abstract

Here a semi-implicit formulation of the gradient augmented level set method is presented. The method is a hybrid Lagrangian--Eulerian method that may be easily applied in two or three dimensions. By tracking both the level set function and the gradient of the level set function, highly accurate descriptions of a moving interface can be formed. Stability is enhanced by the addition of a smoothing term to the gradient augmented level set equations. The new approach allows for the investigation of interfaces evolving by mean curvature and by the intrinsic Laplacian of the curvature. Sample results presented in both two and three dimensions demonstrate the applicability of the scheme. The influence of the smoothing term on stability and accuracy is also investigated.

The three-dimensional jump conditions for the stokes equations with discontinuous viscosity, singular forces, and an incompressible interface

P. Gera and D. Salac
arXiv
September 4, 2013

Abstract

The three-dimensional jump conditions for the pressure and velocity fields, up to the second normal derivative,across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise continuous in the domain while the embedded interface exerts singular forces on the surround fluids. This gives rise to discontinuous solutions in the pressure and velocity field. These jump conditions are required to develop accurate numerical methods, such as the Immersed Interface Method, for the solutions of the Stokes equations in such situations.

Reynolds number effects on lipid vesicles

D. Salac and M.J. Miksis
Journal Paper Journal of Fluid Mechanics, Volume 711, November 2012, Pages 122-146

Abstract

Vesicles exposed to the human circulatory system experience a wide range of flows and Reynolds numbers. Previous investigations of vesicles in fluid flow have focused on the Stokes flow regime. In this work the influence of inertia on the dynamics of a vesicle in a shearing flow is investigated using a novel level-set computational method in two dimensions. A detailed analysis of the behavior of a single vesicle at finite Reynolds number is presented. At low Reynolds numbers the results recover vesicle behavior previously observed for Stokes flow. At moderate Reynolds numbers the classical tumbling behavior of highly viscous vesicles is no longer observed. Instead, the vesicle is observed to tank-tread, with an equilibrium angle dependent on the Reynolds number and the reduced area of the vesicle. It is shown that a vesicle with an inner/outer fluid viscosity ratio as high as 200 will not tumble if the Reynolds number is as low as 10. A new damped tank-treading behavior, where the vesicle will briefly oscillate about the equilibrium inclination angle, is also observed. This behavior is explained by an investigation on the torque acting on a vesicle in shear flow. Scaling laws for vesicles in inertial flows have also been determined. It is observed that quantities such as vesicle tumbling period follow square-root scaling with respect to the Reynolds number. Finally, the maximum tension as a function of the Reynolds number is also determined. It is observed that, as the Reynolds number increases, the maximum tension on the vesicle membrane also increases. This could play a role in the creation of stable pores in vesicle membranes or for the premature destruction of vesicles exposed to the human circulatory system.

A level set projection model of lipid vesicles in general flows

D. Salac and M.J. Miksis
Journal Paper Journal of Computational Physics, Volume 230, Issue 22, September 2011, Pages 8192-8215

Abstract

A new numerical method to model the dynamic behavior of lipid vesicles under general flows is presented. A gradient-augmented level set method is used to model the membrane motion. To enforce the volume- and surface-incompressibility constraints a four-step projection method is developed to integrate the full Navier–Stokes equations. This scheme is implemented on an adaptive non-graded Cartesian grid. Convergence results are presented, along with sample two-dimensional results of vesicles under various flow conditions.

The augmented fast marching method for level set reinitialization

D. Salac
arXiv November 29, 2011

Abstract

Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the fast marching method is presented. This augmented fast marching method will calculate the signed distance function and up to the second-order derivatives of the signed distance function for arbitrary interfaces. In addition to enforcing the condition |∇ϕ|2=1, where ϕ is the level set function, the method ensures that ∇(|∇ϕ|)2=0 and ∇∇(|∇ϕ|)2=0 are also satisfied. Results indicate that for both two- and three-dimensional interfaces the resulting level set and curvature field are smooth even for coarse grids. Convergence results show that using first-order upwind derivatives and the augmented fast marching method result in a second-order accurate level set and gradient field and a first-order accurate curvature field.

A local semi-implicit level-set method for interface motion

D. Salac and W. Lu
Journal Paper Journal of Scientific Computing, Volume 23, Issue 2-3, February 2008, Pages 330-349

Abstract

This paper proposes and implements a novel hybrid level set method which combines the numerical efficiency of the local level set approach with the temporal stability afforded by a semi-implicit technique. By introducing an extraction/insertion algorithm into the local level set approach, we can accurately capture complicated behaviors such as interface separation and coalescence. This technique solves a well known problem when treating a semi-implicit system with spectral methods, where spurious interface movements emerge when two interfaces are close to each other. Numerical experiments show that the proposed method is stable, efficient and scales up well into three dimensional problems.

Stability and shape evolution of voids and channels due to surface misfit

D. Salac and W. Lu
Journal Paper International Journal of Solids and Structures, Volume 45, Issue 13, June 2008, Pages 3793-3806

Abstract

This paper investigates the stability and shape evolution of voids and channels under the combined effects of surface misfit, surface energy and surface diffusion. A dynamic model that incorporates the competition among these energetic forces is developed. Our approach integrates a novel local semi-implicit level set method to capture interface movement and an iterative spectral method to calculate the elastic field, which allows simulating very large shape evolution such as void breakup or coalescence in a wide range of materials systems. Our study reveals the important effect of surface misfit and remarkably rich dynamics during shape evolution. It is shown that surface misfit can lead to instabilities of voids, break-up of channels and ordering of voids.

A level set approach to model directed nanocrack patterns

D. Salac and W. Lu
Journal Paper Computational Materials Science, Volume 39, Issue 4, June 2007, Pages 849-856

Abstract

Recent experiments revealed an exciting possibility of making nanowires by filling nanoscale cracks in a thin film. Exploration and practical application of the method would rely on the modeling capability to predict complex nanocracks and their geometries in heterogeneous films. This paper proposes a level set approach to investigate the formation of nanocrack patterns, which allows precise prediction of the direction of crack extension, geometry of the crack tip, and interaction between crack and other phases. The approach does not require explicit front tracking and allows for the simulation of complex crack patterns and crack intersection. An efficient iterative Fourier spectral method is applied to solve the elastic field. The propagation of the crack interface is determined by the competition between the elastic and interfacial energies. This paper investigates the cracking process in a thin film with etched spaces and stiff phases. Numerical simulations reveal that designed pre-patterns can effectively direct crack extension and suggest a significant degree of experimental control in the formation of nanocrack patterns.

Design nanocrack patterns in heterogeneous films

D. Salac and W. Lu
Journal Paper Nanotechnology, Volume 17, Issue 20, September 2006, Pages 5185-5191

Abstract

Nanowires have significant potential in future technologies such as nanomechanical devices and electronics. Recent experiments suggest that nanowires with sub-100 nm diameters may be fabricated by filling cracks with various materials. The geometry of cracks becomes important on such a length scale, and the practical application of the approach requires an understanding of crack evolution in heterogeneous films. This paper proposes a level-set approach to model directed nanocracks on pre-patterned substrates. The approach does not require the explicit tracking of crack fronts and thus allows the simulation of complex crack patterns. Results indicate that pre-patterning a substrate can lead to various well controlled nanocrack patterns, suggesting a possibility to make designed and complex nanowires difficult to obtain with other methods.

Interactions of metallic quantum dots on a semiconductor substrate

W. Lu and D. Salac
Journal Paper Physical Review B, Volume 74, Issue 7, August 2006, Art. No. 073304

Abstract

Experiments have shown that uniform metallic quantum dots may self-assemble on a semiconductor substrate. The observation calls for a repulsive force when the dots are close. In a traditional quantum dot system, such as Ge dots on a Si substrate, such an action is achieved by elastic interaction. This paper proposes a mechanism for metallic dots without coherent lattice or lattice mismatch, so that elastic effect may not account for the phenomena. We show that electric double layers due to contact potential can lead to size-dependent repulsion, which counterbalances van der Waal attraction and determines feature sizes.

Ordering of metallic quantum dots

D. Salac and W. Lu
Journal Paper Applied Physics Letters, Volume 89, Issue 7, August 2006, Art. No. 073105

Abstract

This letter proposes a mechanism for the ordering of metallic quantum dots without coherent lattice or lattice mismatch with the substrate so that elasticity may not account for the phenomena. The authors show that contact potential induces repulsive charge clouds in the substrate. The size-dependent repulsion and van der Waals attraction lead to ordered nanoscale structures.

Controlled nanocrack patterns for nanowires

D. Salac and W. Lu
Journal Paper Journal of Computational and Theoretical Nanoscience, Volume 3, Issue 2, April 2006, Pages 263-268

Abstract

Recent experiments have shown a new approach of nanowire fabrication by filling cracks with semiconductor materials or metals. Full exploration of this approach calls for a computational model to predict the crack patterns in a thin film. This paper considers crack propagation in a heterogeneous thin film with etched space and stressers for cracking guidance. A phase field model applicable to multiple materials is proposed, which eliminates the need of explicit crack front tracking. The elastic field is solved by an efficient iteration process in Fourier space. The computations show that the propagation direction of nanocracks can be effectively controlled via pre-patterning.

Programmable nanoscale domain patterns in multilayers

D. Salac and W. Lu
Journal Paper Acta Materialia, Volume 53, Issue 11, June 2005, Pages 3253-3260

Abstract

The pattern formation in systems with multiple layers of adsorbate molecules is studied. We consider the presence of two types of molecules in each layer, which are characterized by different dipole moments. The patterns are characterized by the non-uniform distribution of the two molecules. A phase field model is developed to simulate the molecular motion and patterning under the combined actions of dipole moments, intermolecular forces, entropy and external electric field. The study reveals self-alignment, pattern conformation and the possibility to reduce the domain sizes via a layer by layer approach. It is also shown that the pattern in a layer may define the roadway for molecules to travel on top of. This, combined with electrodes embedded in the substrate, gives a great deal of flexibility to guide the molecular motion and patterning.

Patterning multilayers of molecules via self-organization

W. Lu and D. Salac
Journal Paper Physical Review Letters, Volume 94, Issue 14, April 2005, Art. No. 146103

Abstract

The electric dipole interaction among adsorbate molecules may cause them to form regular nanopatterns. In a multilayer system, the self-organization of each layer is also influenced by the underlying layers. This Letter develops a phase field model to simulate the molecular patterning process. The study reveals self-alignment, scaling down of size, and the effect of guided self-assembly with embedded electrodes.

Pattern formation in a polymer thin film induced by an in-plane electric field

D. Salac, W. Lu, C.W. Wang, and A.M. Sastry
Journal Paper Applied Physics Letters, Volume 85, Issue 7, August 2004, Pages 1161-1163

Abstract

This letter reports experimental work involving use of an in-plane electric field to induce morphological patterns in a thin polymer film. The film was first spin coated onto a glass wafer. Then, it was heated to above its glass transition temperature to achieve mobility in the fluid. An in-plane electric field was applied using two parallel electrodes, spaced 10mm apart, whereupon the initially flat polymer∕air interface lost stability and formed islands. The self-assembled islands exhibited a narrow size distribution and demonstrated spatial ordering. We attribute the pattern formation to a combined mechanism of minimization of combined interface energy and electrostatic energy.

Current Teaching

  • Present 2010

    Thermodynamics

    Sophomore level course covering introductory topics in thermodynamics such as the First and Second Laws of Thermodynamics, thermodynamics properties, and physical applications such as internal combustion engines. An online version of the course was developed in 2015 and will be offered yearly thereafter.

  • Present 2010

    Numerical Method for Moving Interfaces

    A graduate level course covering numerical methods to model moving interfaces. Methods covered include marker particle, level set, volume of fluid, and phase field methods. Advance topics related to recent research is also covered.

Teaching History

  • 2015 2015

    Engineering Computations

    This is a course in Linear Algebra and a first course in programming using MATLAB. Upon completion of this course students should have a firm grasp of important topics in Linear Algebra and their application in engineering contexts as well as programming skills in MATLAB, including array manipulation, loop and branching structures, user-defined functions, and plotting.

  • 2010 2008

    Introductory Linear Algebra and MATLAB

    Introduce freshman to linear algebra, including matrix inverse, solution sets, projections, and least squares. Also introduce students to programming using MATLAB. Most students have no previous programming experience.

  • 2008 2007

    Multi-variable Integration and Vector Calculus

    Integration techniques covered included double, triple and surface integrals in polar, cylindrical and spherical coordinates. Vector calculus topics included line integrals, Green’s Theorem, Surface integrals, Divergence Theorem and Stokes’ Theorem.

  • 2010 2008

    Introduction to Ordinary Differential Equations

    Introduces methods to solve ordinary differential equations and first-order systems of ordinary differential equations. The methods are then used to solve engineering applications.

  • 2010 2009

    Numerical Methods for Ordinary Differential Equations

    Introduces numerical methods to solve first-order ordinary differential equations and first-order systems of ordinary differential equations. The methods are then used to solve engineering applications.

Current Laboratory Personel

Prerna Gera

PhD Student

Afsoun Rahnama Falavarjani

PhD Student

Prerna Gera

PhD Student

Afsoun Rahnama Falavarjani

PhD Student

If you are interested in joining the group please contact me.

Prior Laboratory Personel

Mohammadhassan (Moha) Kazemi

MS Project Student

Guhan Velmurugan

MS Thesis Student

Myers Weidner

Summer HS Student

Liam Weidner

Summer HS Student

Ebrahim (Amin) M. Kolahdouz

Former PhD Student

Saman Seifi

Former MS Student

Contact & Meet Me

Feel free to contact me regarding assistance in your research. I am also happy to meet with current and potential students.

  •    Address:

    326 Jarvis, University at Buffalo, Buffalo, New York 14260-4400

  •    Office: 716-645-1460
  •    davidsal .at. buffalo.edu

At My Office

You can find me at my office located at 326 Jarvis Hall, on the North Campus of University at Buffalo.

I am at my office most days from 8:00 am to 4:30 pm. Feel free to contact me to setup an appointment.