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Analysis of relocation mechanisms to overcome the Allee effect

How populations relocate can make a difference between persitence and听extinction.听 We are working in analyzing the best relocation mechanisms to overcome an Allee effect. Our group is also looking at extending these ideas to systems in baby直播apps.听

Territory formation in ecology

We are working on developing techniques to infer movement factors for social ecological species using non-local PDE models.

Gentrification

We are developing models to understand the leading factors that lead to gentrification.听

Dynamics of Violence

We are deloping multi-scale models to mathematize conceptual models for violence put forth by criminologists.听

Modeling Social Outburst

We have developed models to understand the dynamics of social outburts, such as rioting activity.听 These models consist of a social tension field and a level of activity.听 Our current focus is on trying to figure out a way to measure the social tension in real-life in order to predict possible shocks to the system.

NSF Mathematical Sciences Postdoctoral Fellowship, 2011-2014
AWM-NSF Mentoring Travel Grant,听2013
USD McNair Doctoral Achievement Award,听2012
UCLA Graduate Division Fellowship, 2010鈥�2011
NSF VIGRE Fellowship, 2009鈥�2010
Ford Foundation Fellowship, 2006鈥�2009

Rodriguez, N. and Hu, Hh. On the Steady-states of a two-species non-local crossdiffusion model, under review at Journal of Applied Analysis (2019).

Yang, C. and Rodriguez, N. Existence and Stability Traveling Wave Solutions for a System of Social Outbursts, under review at Journal of Nonlinear Science (2018).

Yang, C. and Rodriguez, N. A Numerical Perspective on Traveling Wave Solutions in a System for Rioting Activity, submitted to Applied Mathematics and
Computation (2018).

Hassan, A. and Rodriguez, N. Transport and concentration of wealth: modeling an amenities-based theory, submitted to Mathematical Social Sciences (2019).

Malanson, G. and Rodriguez, N., Traveling waves and spatial patterns from dispersal on homogeneous and gradient habitats, Ecological Complexity, Vol. 33, pg. 57-65 (2018).

Rodriguez, N. and Malanson, G., Plant dynamics, birth-jump processes and sharp traveling waves, Bulletin of Math Biology, Vol. 80, pg. 1655鈥�1687 (2018).

Rodriguez, N. and Winkler, M., On the global existence and qualitative behavior of one-dimensional solutions to a model for urban crime, under review at JMPA, 37 pages (2017).

Bonnasse-Gahot, L., Berestycki, H., Depuiset, M-A., Gordon, M. B., Roch麓e, S., Rodriguez, N., Nadal, J-P., Epidemiological modelling of the 2005 French riots: a spreading wave and the role of contagion, Scientific Reports, online publication 10.1038/s41598-017-18093-4 (2018).

H. Berestycki, N. Rodriguez, and L. Rossi, Periodic cycles of social outburst, Journal of Differential Equations, Vol. 264, pg. 163-196 (2018).

H. Berestycki and N. Rodriguez, Non-local reaction-diffusion equations with a gap, Discrete and Continuous Dynamical Systems-A, Vol. 27, Issue 2, pg. 685-723 (2017).听

H. Berestycki and N. Rodriguez, Analysis of a heterogeneous model for riot dynamics: the effect of censorship of information, European Journal of Applied听Mathematics, Vol. 27, Special Issue 03, pg. 554-582, (2016).

N. Rodriguez and L. Ryzhik, The effect of social preference, mobility, and the environment on segregation, Communications in Mathematical Sciences, Vol. 14, No. 2, pg. 363-387, (2016).

H. Berestycki, J-P. Nadal and N. Rodriguez, A model of riots dynamics: shocks, diffusion and thresholds, Networks and Heterogeneous Media, Vol. 10, No. 3, pg. 443-475, (2015).

N. Rodriguez, Recent advances in mathematical criminology, comment on 鈥淪tatistical physics of crime: A review, by M.R. D鈥橭rsogna and M. Perc鈥�, Physics of Life Review, Vol. 12, pg. 38-39, (2015).

N. Rodriguez, On an Integro-differential model for pest control in a heterogeneous environment, Journal of Mathematical Biology, Vol 70, No. 5, pg. 1177鈥�1206 (2015).

J. Bedrossian and N. Rodriguez, Inhomogeneous Patlak-Keller-Segel models and aggregation equations with nonlinear diffusion in Rd, Discrete and Continuous Dynamical Systems-B, Vol. 19, No. 24, pg. 1279鈥�1309 (2014).

H. Berestycki, N. Rodriguez and L. Ryzhik, Traveling wave solutions in a reactiondiffusion model for criminal activity, Multiscale Modeling and Simulations, Vol. 11, Issue 4, pg. 1097-1126, (2013).

N. Rodriguez, On the global well-posedness theory for a class of PDE models for criminal activity, Physica D: Nonlinear Phenomena, pg. 191-200, (2013).
J. Bedrossian, N. Rodriguez and A. Bertozzi, Local and global well-posedness for aggregation equations and Patlak-Keller-Segel models with degenerate diffusion, Nonlinearity, Vol. 24, No. 6, pg. 1683-1714, (2011).

N. Rodriguez and A. Bertozzi, Local existence and uniqueness of solutions to a PDE model for criminal behavior, M3AS, special issue on Mathematics and Complexity in Human and Life Sciences, Vol 20, Issue supp01, pg. 1425鈥�1457,听(2010).

A.P. Velo, G.A. Gazonas, E. Bruder and N. Rodriguez, Recursive dispersion relations in one-dimensional periodic elastic media, SIAM Journal on Applied Mathematics, Vol. 69, No. 3, pg. 670鈥�689, (2007).