Grigor Nika
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View article: Simulation of effective scale-size dependent heat conduction in rigid microgeometries
Simulation of effective scale-size dependent heat conduction in rigid microgeometries Open
We present homogenization and simulation results for an enhanced heat equation model that captures thermal scale-size effects through higher-gradient corrections involving characteristic internal lengths. The resulting equation is a fourt…
View article: Mathematics for energy systems: Methods, modeling strategies, and simulation
Mathematics for energy systems: Methods, modeling strategies, and simulation Open
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior. …
View article: A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation
A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation Open
We present a finite-volume based numerical scheme for a nonlocal Cahn–Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn–Hilliard equations. The equation of interest is a spec…
View article: Scale-size dependent multi-continuum homogenization of complex bodies
Scale-size dependent multi-continuum homogenization of complex bodies Open
We derive effective equations of a periodically heterogeneous Cosserat material encompassing intrinsic lengths modelling scale-size effects. The resultant homogenized material supports internal body torques and leads to an asymmetric effec…
View article: A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn-Hilliard Equation
A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn-Hilliard Equation Open
We present a finite-volume based numerical scheme for a nonlocal Cahn-Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn-Hilliard equations. The equation of interest is a spec…
View article: Effective medium theory for second-gradient elasticity with chirality
Effective medium theory for second-gradient elasticity with chirality Open
We derive effective models for a heterogeneous second-gradient elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four characteristic lengths: The size …
View article: On a hierarchy of effective models for the biomechanics of human compact bone tissue
On a hierarchy of effective models for the biomechanics of human compact bone tissue Open
We derive a hierarchy of effective models that can be used to model the biomechanics of human compact bone taking into account scale-size effects observed experimentally. The classification of the effective models depends on the hierarchy …
View article: A gradient system for a higher-gradient generalization of Fourier’s law of heat conduction
A gradient system for a higher-gradient generalization of Fourier’s law of heat conduction Open
We derive a generalized heat conduction problem for a rarefied gas at slip regime from a gradient system where the driving functional is the entropy. Specifically, we construct an Onsager system [Formula: see text] such that the associated…
View article: Hypertemperature effects in heterogeneous media and thermal flux at small-length scales
Hypertemperature effects in heterogeneous media and thermal flux at small-length scales Open
We propose an enriched microscopic heat conduction model that can account for size effects in heterogeneous media. Benefiting from physically relevant scaling arguments, we improve the regularity of the corrector in the classical problem o…
View article: Hypertemperature effects in heterogeneous media and thermal flux at small-length scales
Hypertemperature effects in heterogeneous media and thermal flux at small-length scales Open
We employ an enriched microscopic heat conduction model that can account for size effects in heterogeneous media. Through, physically, relevant scaling arguments we improve the regularity of the corrector in the classical problem of period…
View article: Cosserat continuum modelling of chiral scale-size effects and their influence on effective constitutive laws
Cosserat continuum modelling of chiral scale-size effects and their influence on effective constitutive laws Open
We derive effective models from heterogeneous Cosserat media using asymptotic homogenization and taking into account size effects observed experimentally. The classification of the effective equations depends on the hierarchy of four chara…
View article: Effective medium theory for second-gradient elasticity with chirality
Effective medium theory for second-gradient elasticity with chirality Open
We derive effective, parsimonious models from a heterogeneous second-gradient nonlinear elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four characte…
View article: A coarse‐grained electrothermal model for organic semiconductor devices
A coarse‐grained electrothermal model for organic semiconductor devices Open
We derive a coarse‐grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift‐diffusion‐ based electrothermal models with thermistor‐type models on subregions of the device and suitable …
View article: Derivation of effective models from heterogenous Cosserat media via periodic unfolding
Derivation of effective models from heterogenous Cosserat media via periodic unfolding Open
We derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we pro…
View article: Derivation of effective models from heterogenous Cosserat media via periodic unfolding
Derivation of effective models from heterogenous Cosserat media via periodic unfolding Open
We derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we pro…
View article: Design of thin micro-architectured panels with extension-bending coupling effects using topology optimization
Design of thin micro-architectured panels with extension-bending coupling effects using topology optimization Open
We design thin micro-architectured panels with programmable macroscopic behaviour using inverse homogenization, the Hadamard shape derivative, and a level set method in the diffuse interface context. The optimally designed microstructures …
View article: A hybrid model for the electrothermal behavior of semiconductor devices
A hybrid model for the electrothermal behavior of semiconductor devices Open
We introduce a hybrid model for the electro‐thermal behavior of semiconductor heterostructures. It combines a model based on drift‐diffusion with thermistor type models in different subregions of the semiconductor device. The aim of this h…
View article: An existence result for a class of nonlinear magnetorheological composites
An existence result for a class of nonlinear magnetorheological composites Open
We prove existence of a weak solution for a nonlinear, multi-physics, multi-scale problem of magnetorheological suspensions introduced in Nika & Vernescu (Z. Angew. Math. Phys., 71(1):1--19, '20). The hybrid model couples the Stokes' equat…
View article: Dimension reduction of thermistor models for large-area organic light-emitting diodes
Dimension reduction of thermistor models for large-area organic light-emitting diodes Open
An effective system of partial differential equations describing the heat and current flow through a thin organic light-emitting diode (OLED) mounted on a glass substrate is rigorously derived from a recently introduced fully three-dimensi…
View article: OPTIMAL DESIGN OF AUXETIC, ADDITIVELY MANUFACTURED, POLYMERIC STRUCTURES
OPTIMAL DESIGN OF AUXETIC, ADDITIVELY MANUFACTURED, POLYMERIC STRUCTURES Open
This work is concerned with the optimal design, additive manufacturing, and testing of microarchitectured polymer materials with desired macroscopic mechanichal properties. More precise, we are interested in designing and fabricating a mat…
View article: Rate of convergence for a multi-scale model of dilute emulsions with non-uniform surface tension
Rate of convergence for a multi-scale model of dilute emulsions with non-uniform surface tension Open
In this paper we are interested in a problem of dilute emulsions of two immiscible viscous fluids, in which one is distributed in the other in the form of droplets of arbitrary shape, with non-uniform surface tension due to surfactants. Th…
View article: Multiscale analysis of emulsions and suspensions with surface effects
Multiscale analysis of emulsions and suspensions with surface effects Open
The better understanding of the behavior of emulsions and suspensions is important in many applications. In general, emulsions allow the delivery of insoluble agents to be uniformly distributed in a more efficient way. At the same time sus…