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+34 946 567 842
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+34 946 567 843
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rmelnik@bcamath.org
Information of interest
Research interests include:
- Mathematical models in nanoscience, new technologies, and life science applications;
- Nanoscale systems and low dimensional nanostructures in particular;
- Coupled dynamic phenomena, systems, and processes;
- Complex dynamic systems.
For more information see the above website.
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Coupled stochastic systems of Skorokhod type: well-posedness of a mathematical model and its applications
Thieu, T.K.T; Muntean, A.; Melnik, R.
(2022)
Population dynamics with complex biological interactions, accounting for uncertainty quantification, is critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation ...
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Effects of noise on leaky integrate-and-fire neuron models for neuromorphic computing applications
Thieu, T.K.T; Melnik, R. (2022)
Artificial neural networks (ANNs) have been extensively used for the description of problems arising from biological systems and for constructing neuromorphic computing models. The third generation of ANNs, namely, ...
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Effects of random inputs and short-term synaptic plasticity in a LIF conductance model for working memory applications
Thieu, TKT.; Melnik, R. (2022)
Working memory (WM) has been intensively used to enable the temporary storing of information for processing purposes, playing an important role in the execution of various cognitive tasks. Recent studies have shown that ...
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Nonlocal Models in the Analysis of Brain Neurodegenerative Protein Dynamics with Application to Alzheimer's Disease
Pal, S.; Melnik, R. (2021)
It is well known that today nearly one in six of the world’s population has to deal with neurodegenerative disorders. While a number of medical devices have been developed for the detection, prevention, and treatments of ...
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The topology of higher-order complexes associated with brain hubs in human connectomes
Andjelkovic, M.; Bosiljka, T.; Melnik, R. (2020-12-01)
Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry ...
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Modeling latent infection transmissions through biosocial stochastic dynamics
Melnik, R.; Tadic, B. (2020-08)
The events of the recent SARS-CoV-2 epidemics have shown the importance of social factors, especially given the large number of asymptomatic cases that effectively spread the virus, which can cause a medical emergency to ...
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Atomistic to continuum model for studying mechanical properties of RNA nanotubes
Badua, S.; Prabhakara, S.; Melnik, R.; Singha, S. (2020-06)
With rapid advancements in the emerging field of RNA nanotechnology, its current and potential applications, new important problems arise in our quest to better understand properties of RNA nanocomplexes. In this paper, ...
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Thermal ablation of biological tissues in disease treatment: A review of computational models and future directions
Singha, S.; Melnik, R. (2020-03)
Percutaneous thermal ablation has proved to be an effective modality for treating both benign and malignant tumors in various tissues. Among these modalities, radiofrequency ablation (RFA) is the most promising and widely ...
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Functional Geometry of Human Connectomes
Tadic, B.; Andjelkovic, M.; Melnik, R. (2019-08)
Mapping the brain imaging data to networks, where nodes represent anatomical brain regions and edges indicate the occurrence of fiber tracts between them, has enabled an objective graph-theoretic analysis of human connectomes. ...
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Computational Analysis of Pulsed Radiofrequency Ablation in Treating Chronic Pain
Singh, S.; Melnik, R. (2019-06)
In this paper, a parametric study has been conducted to evaluate the effects of frequency and duration of the short burst pulses during pulsed radiofrequency ablation (RFA) in treating chronic pain. Affecting the brain and ...
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Radiofrequency Ablation for Treating Chronic Pain of Bones: Effects of Nerve Locations
Singh, S.; Melnik, R. (2019-05)
The present study aims at evaluating the effects of target nerve location from the bone tissue during continuous radiofrequency ablation (RFA) for chronic pain relief. A generalized three-dimensional heterogeneous computational ...
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Ab-initio calculations of strain induced relaxed shape armchair graphene nanoribbon
Prabhakar, S.; Melnik, R. (2019)
An odd number of zigzag edges in armchair graphene nanoribbons and their mechanical properties (e.g., Young's modulus, Poisson ratio and shear modulus) have potential interest for bandgap engineering in graphene based ...
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Coupled thermo-electro-mechanical models for thermal ablation of biological tissues and heat relaxation time effects
Singh, S.; Melnik, R. (2019)
Thermal ablation is a widely applied electrosurgical process in medical treatment of soft biological tissues. Numerical modeling and simulations play an important role in prediction of temperature distribution and ...
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Valley-dependent Lorentz force and Aharonov-Bohm phase in strained graphene p-n junction
Prabhakar, S.; Nepal, R.; Melnik, R.; Kovalev, A.A. (2019)
Veselago lens focusing in graphene p-n junction is promising for realizations of new generation electron optics devices. However, the effect of the strain-induced Aharonov-Bohm interference in a p-n junction has not been ...
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Spectral properties of hyperbolic nano-networks with tunable aggregation of simplexes
Dankulov, M.M.; Tadic, B.; Melnik, R. (2019)
Cooperative self-assembly is a ubiquitous phenomenon found in natural systems which is used for designing nanostructured materials with new functional features. Its origin and mechanisms, leading to improved functionality ...
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Modeling microstructure evolution in shape memory alloy rods via Legendre wavelets collocation method
He, X.; Tong, Z.; Du, H.; Wang, D.; Wang, L.X.; Melnik, R. (2019)
Microstructures play an important role in the research on shape memory alloys (SMA). By using mathematical modeling tools to study microstructures, it is possible to predict the behaviors of these materials under applied ...
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Parametric Vibration Analysis of Pipes Conveying Fluid by Nonlinear Normal Modes and a Numerical Iterative Approach
Liang, F.; Yang XD; Zhang, W.; Qian, Y.J.; Melnik, R. (2019)
Nonlinear normal modes and a numerical iterative approach are applied to study the parametric vibrations of pipes conveying pulsating fluid as an example of gyroscopic continua. The nonlinear non-autonomous governing ...
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Berry phase and spin precession without magnetic fields in semiconductor quantum dots
Prabhakar, S.; Melnik, R. (2019)
We investigate electric field control of spin manipulation through Berry phase in III-V semiconductor quantum dots. By utilizing degenerate and non-degenerate perturbation theories, we diagonalize the total Hamiltonian of ...
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Coupled Electro-mechanical Behavior of Microtubules
Singh, S.; Melnik, R. (2019)
n this contribution, the coupled electro-mechanical behavior of the microtubules has been systematically investigated utilizing a continuum-based finite element framework. A three-dimensional computational model of a mi- ...
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Hidden electronic rule in the "cluster-plus-glue-Atom" model
Du, J.; Dong, C.; Melnik, R.; Kawazoe, Y.; Wen, B. (2016-10-01)
Electrons and their interactions are intrinsic factors to affect the structure and properties of materials. Based on the “cluster-cluster-plus-glue-atom” model, an electron counting rule for complex metallic alloys (CMAs) ...
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Pseudospin lifetime in relaxed-shape armchair graphene nanoribbons due to in-plane phonon modes
Prabhakar, S.; Melnik, R.; Bonilla, L. (2016-01-01)
We study the influence of ripple waves on the band structures of strained armchair graphene nanoribbons. We argue that the Zeeman pseudospin (p-spin) splitting energy induced by ripple waves might not be neglected for ...
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Corrections to finite-size scaling in the $\varphi^4$ model on square lattices
Kaupuzs, J.; Melnik, R.; Rimsans, J. (2016-01-01)
Corrections to scaling in the two-dimensional (2D) scalar (Formula presented.) model are studied based on nonperturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L ((Formula ...
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On the Perturbation Methods for Vibration Analysis of Linear Time-Varying Systems
Yang, X.-D.; Liu, M.; Zhang, W.; Qian, Y.J.; Melnik, R. (2016-01-01)
Some perturbation methods in the studying vibrations of the linear time-varying (LTV) system are discussed. Three classical perturbation methods, namely, averaging method, harmonic balance method, and multiple scales method ...
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Tuning $g$-factor of electrons through spin-orbit coupling in GaAs/AlGaAs conical quantum dots
Prabhakar, S.; Melnik, R. (2016-01-01)
We investigate band structures of (Formula presented.) three-dimensional conical quantum dots (QDs). In particular, we explore the influence of the Rashba and Dresselhaus spin–orbit couplings in the variation of effective ...
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Electrochemical Potential Derived from Atomic Cluster Structures
Du, J.; Xiao, D.; Wen, B.; Melnik, R.; Kawazoe, Y. (2016-01-01)
Based on the atomic cluster structures and free electron approximation model, it is revealed that the electrochemical potential (ECP) for the system of interest is proportional to the reciprocal of atomic cluster radius ...
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Three Dimensional Metallic Carbon from Distorting sp3-Bond
Cheng, Y.; Melnik, R.; Kawazoe, Y.; Wen, B. (2016-01-01)
Owing to the outstanding properties of metallic carbon as well as their great potential applications, design and synthesis of metallic carbon have long attracted considerable attention. In this work, a new three-dimensional ...
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Mechanism of hydrogen production via water splitting on 3C-SiC's different surfaces: A first-principles study
Du, J.; Wen, B.; Melnik, R. (2014-12-31)
The reaction mechanism of producing hydrogen via water splitting on the different surfaces of cubic silicon carbide (3C-SiC), the adsorption energy and the activation energy have been studied here by using density functional ...
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Coupled magneto-thermo-electromechanical effects and electronic properties of quantum dots
Prabhakar, S.; Melnik, R.; Neittaanmäki, P.; Tiihonen, T. (2013-12-31)
For the first time, we systemically analyze the influence of magneto-thermo-electromechanical effects on the band structure calculations by using the fully coupled model. We focus on three different types of quantum dots ...
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Computational aspects of Monte-Carlo simulations of the first passage time for multivariate transformed Brownian motions with jumps
Zhang, D.; Melnik, R. (2013-12-31)
Many problems in science, engineering, and finance require the information on the first passage time (FPT) of a stochastic process. Mathematically, such problems are often reduced to the evaluation of the probability density ...
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Molecular dynamics study on ZnO nanowires mechanical properties: Strain rate, temperature and size dependent effects
Guo, J.; Wen, B.; Melnik, R. (2012-12-31)
Using molecular dynamics simulations, strain rate, temperature, size and orientation dependent mechanical properties of zinc oxide (ZnO) nanowire are carried out with tensile loading. It is found that, for the same ...
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Nonlinear dynamics of shape memory alloy oscillators in tuning structural vibration frequencies
Wang, L.; Melnik, R. (2012-12-31)
Shape memory alloy (SMA) is one of the novel advanced functional materials that has an increasing range of current and potential applications, including smart materials and structures, bio-medical and nanotechnologies. ...
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Excitation of plasmons in a two-dimensional electron gas with defects by microwaves: Wake-field method
Takhtamirov, E.; Melnik, R. (2011-12-31)
We develop an analytical method to find plasmons generated by microwaves in a two-dimensional electron gas with defects. The excitations are expressed in terms of the wake field of a charged particle moving in plasma. The ...
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Molecular dynamics study on diamond nanowires mechanical properties: Strain rate, temperature and size dependent effects
Guo, J.; Wen, B.; Melnik, R.; Yao, S.; Li, T. (2011-12-31)
Using molecular dynamics simulations, strain rate, temperature and size dependent mechanical properties of < 001 > orientation diamond nanowires are investigated. It is found that, for the same cross-sectional areas, ...
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Stress induced polarization switching and coupled hysteretic dynamics in ferroelectric materials
Wang, L.; Melnik, R.; Lv, F. (2011-12-31)
The dynamic responses of ferroelectric materials upon external mechanical and electrical stimulations are inherently nonlinear and coupled. In the current paper, a macroscopic differential model is constructed for the ...
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Higher-order nonlinear electromechanical effects in wurtzite GaN/AlN quantum dots
Bahrami-Samani, M.; Patil, S.R.; Melnik, R. (2010-12-31)
As we demonstrated earlier, conventional mathematical models based on linear approximations may be inadequate in the analysis of properties of low-dimensional nanostructures and band structure calculations. In this work, ...
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Manipulation of single electron spin in a GaAs quantum dot through the application of geometric phases: The Feynman disentangling technique
Prabhakar, S.; Raynolds, J.; Inomata, A.; Melnik, R. (2010-12-31)
The spin of a single electron in an electrically defined quantum dot in a two-dimensional electron gas can be manipulated by moving the quantum dot adiabatically in a closed loop in the two-dimensional plane under the ...
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Spin-orbit interaction in three-dimensionally bounded semiconductor nanostructures
Takhtamirov, E.; Melnik, R. (2010-12-31)
The structural inversion asymmetry-induced spin-orbit interaction of conduction band electrons in zinc-blende and wurtzite semiconductor structures is analysed allowing for a three-dimensional (3D) character of the external ...
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Coarse-graining RNA nanostructures for molecular dynamics simulations
Paliy, M.; Melnik, R.; Shapiro, B.A. (2010-12-31)
A series of coarse-grained models have been developed for study of the molecular dynamics of RNA nanostructures. The models in the series have one to three beads per nucleotide and include different amounts of detailed ...
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Numerical analysis of complex systems evolution with phase transformations at different spatial scales
Melnik, R.; Dhote, R.P.; Zu, J.; Tsviliuk, O.I.; Wang, L.X. (2010-12-31)
This paper shows the existence of a critical dimension for finite length nanowires exhibiting shape memory effects. We give a brief survey of phase transformations, their classifications, and provide the basis of mathematical ...
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Influence of electromechanical effects and wetting layers on band structures of AlN/GaN quantum dots and spin control
Prabhakar, S.; Melnik, R. (2010-12-31)
In a series of recent papers we demonstrated that coupled electromechanical effects can lead to pronounced contributions in band structure calculations of low dimensional semiconductor nanostructures (LDSNs) such as quantum ...
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Microstructures of constrained shape memory alloy nanowires under thermal effects
Dhote, R.P.; Melnik, R.; Zu, J.W.; Wang, L. (2010-12-31)
In this paper, martensitic transformations in constrained Fe-Pd nanowires are studied using a mesoscopic model analyzed in detail numerically in our earlier papers. The dynamics of squareto-rectangular transformation is ...
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Geometry and temperature dependent thermal conductivity of diamond nanowires: A non-equilibrium molecular dynamics study
Guo, J.; Wen, B.; Melnik, R.; Yao, S.; Li, T. (2010-12-31)
Using non-equilibrium molecular dynamics methods, the analysis of geometry and temperature dependent thermal conductivities of diamond nanowires is carried out. It is found that at the same temperature conditions, thermal ...
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Complex systems in finance: Monte Carlo evaluation of first passage time density functions
Tsviliuk, O.; Zhang, D.; Melnik, R. (2010-12-31)
Many examples of complex systems are provided by applications in finance and economics areas. Some of intrinsic features of such systems lie with the fact that their parts are interacting in a non-trivial dynamic manner ...
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Band structures of laterally coupled quantum dots, accounting for electromechanical effects
Prabhakar, S.; Melnik, R.; Patil, S. (2010-12-31)
In a series of recent papers we demonstrated that coupled electro-mechanical effects can lead to pronounced contributions in band structure calculations of low dimensional semiconductor nanostructures (LDSNs) such as quantum ...
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Band structures of cylindrical AlN/GaN quantum dots with fully coupled piezoelectric models
Prabhakar, S.; Melnik, R. (2010-12-31)
We study the coupled electro-mechanical effects in the band structure calculations of low dimensional semiconductor nanostructures (LDSNs) such as AlN/GaN quantum dots. Some effects in these systems are essentially nonlinear. ...
- Machine-Learning-Driven Atomistic Simulations for Energy and Biomedical Applications
| Date | Title | Place | Author/s | Type | |
| 2020-07-19 |
Multidisciplinary alliance in biosciences: modeling, computing, technology and clinical applications |
Paris, France (at WCCM14/ECCOMAS-2020) | News and Events | ||
| 2020-05-18 | Predictive Multiscale Materials Design with Mathematical Modelling and Machine Learning | Bilbao, Spain (at SIAM Conference MS20) | News and Events | ||
| 2019-08-19 |
The Vth International AMMCS Conference / Interdisciplinary AMMCS Conference Series |
Waterloo, Canada | News and Events | ||
| 2018-04-01 | Focus Program on Nanoscale Systems and Coupled Phenomena: Mathematical Analysis, Modeling, and Applications | Toronto, Canada (Fields Institute) | News and Events | ||
| 2016-08-28 | Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications |
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News and Events |