# Fernando Guevara VasquezUniversity of Utah | UOU · Department of Mathematics

Fernando Guevara Vasquez

phd

## About

56

Publications

8,285

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1,188

Citations

Citations since 2017

## Publications

Publications (56)

Ultrasound directed self-assembly (DSA) allows organizing particles dispersed in a fluid medium into user-specified patterns, driven by the acoustic radiation force associated with a standing ultrasound wave. Accurate control of the spatial organization of the particles in the fluid medium requires accounting for medium viscosity and particle volum...

We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same...

We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active, we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a...

We theoretically show that a superposition of plane waves causes small (compared to the wavelength) particles dispersed in a fluid to assemble in quasiperiodic two or three-dimensional patterns. We experimentally demonstrate this theory by using ultrasound waves to assemble quasiperiodic patterns of carbon nanoparticles in water using an octagonal...

We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a d...

We theoretically show that a superposition of plane waves causes small (compared to the wavelength) particles dispersed in a fluid to assemble in quasiperiodic two or three dimensional patterns. We experimentally demonstrate this theory by using ultrasound waves to assemble quasiperiodic patterns of carbon nanoparticles in water using an octagonal...

Ultrasound directed self-assembly (DSA) enables noninvasively aligning high aspect ratio particles in three-dimensional (3D) user-specified orientations, which finds application in a myriad of engineering applications, including manufacturing engineered materials. However, the number of ultrasound transducers and their spatial arrangement limit the...

Ultrasound-directed self-assembly (DSA) enables particles to be arranged into user-specified patterns, which finds application in a myriad of engineering applications. However, using ultrasound DSA with nonspherical particles requires the ability to explicitly control their orientation. We theoretically derive a method to determine the operating pa...

We determine crystal-like materials that can be fabricated by using a standing acoustic wave to arrange small particles in a non-viscous liquid resin, which is cured afterwards to keep the particles in the desired locations. For identical spherical particles with the same physical properties and small compared to the wavelength, the locations where...

We experimentally demonstrate a ~1 mm-thick near-infrared (NIR) camera comprised of a multi-level diffractive lens coupled with a conventional monochrome image sensor. We performed careful measurements of the point-spread function, the modulation transfer function, focusing efficiency, aberrations and the field of view of the camera.

Significance
We demonstrate, with simulations corroborated by experiments, that broadband long-wave infrared (LWIR) imaging is possible with a single flat lens with a thickness of 10 μm and a weight that is over 100 times less than conventional refractive optics. Reducing the weight and thickness of LWIR optics is crucial for increasing the range o...

We determine crystal-like materials that can be fabricated by using a standing acoustic wave to arrange small particles in a non-viscous liquid resin, which is cured afterwards to keep the particles in the desired locations. For identical spherical particles with the same physical properties and small compared to the wavelength, the locations where...

Recently, there has been an explosion of interest in metalenses for imaging. The interest is primarily based on their subwavelength thicknesses. Diffractive gratings have been used as thin optical elements since the late 19th century. Here, we show that multilevel diffractive lenses (MDLs), when designed properly, can exceed the performance of meta...

We experimentally demonstrate imaging in the longwave-infrared (LWIR) spectral band (8um to 12um) using a single polymer flat lens based upon multi-level diffractive optics. The device thickness is only 10{\mu}m, and chromatic aberrations are corrected over the entire LWIR band with one surface. Due to the drastic reduction in device thickness, we...

We consider the inverse problem of finding matrix valued edge or nodal quantities in a graph from measurements made at a few boundary nodes. This is a generalization of the problem of finding resistors in a resistor network from voltage and current measurements at a few nodes, but where the voltages and currents are vector valued. The measurements...

We present a method for imaging small scatterers in a homogeneous medium from polarization measurements of the electric field at an array. The electric field comes from illuminating the scatterers with a point source with known location and polarization. We view this problem as a generalized phase retrieval problem with data being the coherency mat...

We consider the problem of approximating a function using Herglotz wave functions, which are a superposition of plane waves. When the discrepancy is measured in a ball, we show that the problem can essentially be solved by considering the function we wish to approximate as a source distribution and time reversing the resulting field. Unfortunately...

Particles dispersed in a fluid medium are organized into three-dimensional (3D) user-specified patterns using ultrasound directed self-assembly. The technique employs standing ultrasoundwave fields created by ultrasound transducers that line the boundary of a fluid reservoir. The acoustic radiation force associated with the standing ultrasoundwave...

We present a method for imaging the polarization vector of an electric dipole distribution in a homogeneous medium from measurements of the electric field made at a passive array. We study an electromagnetic version of Kirchhoff imaging and prove, in the Fraunhofer asymptotic regime, that range and cross-range resolution estimates are identical to...

We use ultrasound directed self-assembly to organize particles dispersed in a fluid medium into a three-dimensional (3D) user-specified pattern. The technique employs ultrasound transducers that line the boundary of a fluid reservoir to create a standing ultrasound wave field. The acoustic radiation force associated with the wave field drives parti...

We demonstrate a method of unconstrained manipulation of a spherical microparticle submerged in a fluid medium using a standing ultrasound wave field. The method works by displacing the microparticle in small increments through independent adjustment of the phases and amplitudes of two opposing ultrasound transducers. We model the dynamic behavior...

We employ an ultrasound wave field generated by one or more ultrasound transducers to organize large quantities of nanoparticles dispersed in a fluid medium into two-dimensional user-specified patterns. To accomplish this, we theoretically derive a direct method of calculating the ultrasound transducer parameters required to assemble a user-specifi...

We employ an ultrasoundwave field generated by one or more ultrasound transducers to organize large quantities of nanoparticles dispersed in a fluid medium into two-dimensional user-specified patterns. To accomplish this, we theoretically derive a direct method of calculating the ultrasound transducer parameters required to assemble a user-specifie...

We propose a discrete approach for solving an inverse problem for Schr\"odinger's equation in two dimensions, where the unknown potential is to be determined from boundary measurements of the Dirichlet to Neumann map. For absorptive potentials, and in the continuum, it is known that by using the Liouville identity we obtain an inverse conductivity...

We present a simple, frequency domain, preprocessing step to Kirchhoff
migration that allows the method to image scatterers when the wave field phase
information is lost at the receivers, and only intensities are measured. The
resulting imaging method does not require knowing the phases of the probing
field or manipulating the phase of the wave fie...

We study the uniqueness question for two inverse problems on graphs. Both problems consist in finding (possibly complex) edge or nodal based quantities from boundary measurements of solutions to the Dirichlet problem associated with a weighted graph Laplacian plus a diagonal perturbation. The weights can be thought of as a discrete conductivity and...

By introducing an ultra-thin diffractive filter, a compact snapshot hyper-spectral imager is built and characterized. It is enabled by a fast computational algorithm and offers high-resolution, high-throughput real-time imaging and also 3D imaging.

We study the uniqueness question for two inverse problems on graphs. Both
problems consist in finding (possibly complex) edge or nodal based quantities
from boundary measurements of solutions to the Dirichlet problem associated
with a weighted graph Laplacian plus a diagonal perturbation. The weights can
be thought of as a discrete conductivity and...

Scatterers in a homogeneous medium are imaged by probing the medium with two
point sources of waves modulated by correlated signals and by measuring only
intensities at one single receiver. For appropriately chosen source pairs, we
show that full waveform array measurements can be recovered from such intensity
measurements by solving a linear least...

The objective of this study is to apply an inverse analysis using the iTOUGH2 model to estimate the location of a leakage pathway in multiple brine reservoirs when CO2 is injected. If a reservoir exhibits leakage, brine or CO2 is able to migrate into a permeable reservoir overlying the storage reservoir. Fluid pressure anomalies induced by leaks in...

We analyze the dynamic behavior of a spherical microparticle submerged in a fluid medium, driven to the node of a standing bulk acoustic wave created by two opposing transducers. We derive the dynamics of the fluid-particle system taking into account the acoustic radiation force and the time-dependent and time-independent drag force acting on the p...

The isospectral reduction of matrix, which is closely related to its Schur
complement, allows to reduce the size of a matrix while maintaining its
eigenvalues up to a known set. Here we generalize this procedure by increasing
the number of possible ways a matrix can be isospectrally reduced. The reduced
matrix has rational functions as entries. We...

Convergence and stability results for the inverse Born series [Moskow and
Schotland, Inverse Problems, 24:065005, 2008] are generalized to mappings
between Banach spaces. We show that by restarting the inverse Born series one
obtains a class of iterative methods containing the Gauss-Newton and
Chebyshev-Halley methods. We use the generalized invers...

A method of unconstrained and continuous manipulation of micro-particles in a fluid using bulk acoustic waves is theoretically derived and experimentally demonstrated. The method is based on phase-control of standing pressure waves created by two opposing transducers. Reflections are taken into account, removing the need for complex experiments. Th...

Quorum sensing is the process by which bacteria regulate their gene expression based on the local cell-population density. The quorum sensing systems of Vibrio harveyi and Vibrio cholerae are comprised of a phosphorelay cascade coupled to a small RNA (sRNA) circuit. The sRNA circuit contains multiple quorum regulated small RNA (Qrr) that regulate e...

We consider damped elastodynamic networks where the damping matrix is assumed
to be a non-negative linear combination of the stiffness and mass matrices
(also known as Rayleigh or proportional damping). We give here a
characterization of the frequency response of such networks. We also answer the
synthesis question for such networks, i.e., how to c...

We design a device that generates fields canceling out a known probing field
inside a region to be cloaked while generating very small fields far away from
the device. The fields we consider satisfy the Laplace equation, but the
approach remains valid in the quasistatic regime in a homogeneous medium. We
start by relating the problem of designing a...

We review a resistor network approach to the numerical solution of the
inverse problem of electrical impedance tomography (EIT). The networks arise in
the context of finite volume discretizations of the elliptic equation for the
electric potential, on sparse and adaptively refined grids that we call
optimal. The name refers to the fact that the gri...

This chapter consists of three parts. In the first part we recall the
elastodynamic equations under coordinate transformations. The idea is to use
coordinate transformations to manipulate waves propagating in an elastic
material. Then we study the effect of transformations on a mass-spring network
model. The transformed networks can be realized wit...

We present a study of the numerical solution of the two dimensional
electrical impedance tomography problem, with noisy measurements of the
Dirichlet to Neumann map. The inversion uses parametrizations of the
conductivity on optimal grids. The grids are optimal in the sense that finite
volume discretizations on them give spectrally accurate approxi...

We introduce an inversion algorithm for electrical impedance tomography (EIT) with partial boundary measurements, in two dimensions. It gives stable and fast reconstructions using sparse parameterizations of the unknown conductivity on optimal grids that are computed as part of the inversion. We follow the approach in [8, 27] that connects inverse...

We cloak a region from a known incident wave by surrounding the region with
three or more devices that cancel out the field in the cloaked region without
significantly radiating waves. Since very little waves reach scatterers within
the cloaked region, the scattered field is small and the scatterers are for all
practical purposes undetectable. The...

The response function of a network of springs and masses, an elastodynamic network, is the matrix valued function $W(\omega)$, depending on the frequency $\omega$, mapping the displacements of some accessible or terminal nodes to the net forces at the terminals. We give necessary and sufficient conditions for a given function $W(\omega)$ to be the...

It is shown how a recently proposed method of cloaking is effective over a
broad range of frequencies. The method is based on three or more active
devices. The devices, while not radiating significantly, create a ``quiet
zone'' between the devices where the wave amplitude is small. Objects placed
within this region are virtually invisible. The cloa...

A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to findi...

A new method of cloaking is presented. For two-dimensional quasistatics
it is proven how a single active exterior cloaking device can be used to
shield an object from surrounding fields, yet produce very small
scattered fields. The problem is reduced to finding a polynomial which
is approximately one within one disk and zero within a second disk, a...

Radio Tomographic Imaging (RTI) is an emerging technology that uses received signal strength measurements to image the attenuation of objects within a wireless network area. RTI is by nature an ill-posed inverse problem, therefore, regularization techniques must be utilized to obtain accurate images. This paper discusses some com-mon regularization...

We introduce a novel inversion algorithm for electrical impedance tomography in two dimensions, based on a model reduction approach. The reduced models are resistor networks that arise in five point stencil discretizations of the elliptic partial differential equation satisfied by the electric potential, on adaptive grids that are computed as part...

We use the singular value decomposition of the array response matrix, frequency by frequency, to im- age selectively the edges of extended reflectors in a homogeneous medium. We show with numerical simulations in an ultrasound regime, and analytically in the Fraunhofer diffraction regime, that infor- mation about the edges is contained in the singu...

We propose a robust interpolation scheme for non-overlapping two-level domain decomposition methods applied to two-dimensional elliptic problems with discontinuous coefficients. This interpolation is used to design a preconditioner closely related to the BPS scheme proposed in J. H. Bramble, J. E. Pasciak and A. H. Schatz [Math. Comput. 47, 103-134...

## Projects

Project (1)