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Chauhan AS, Singhania RR, Patel AK, Bhatia SK, Chang JS, Chen CW, Dong CD. A sustainable bioremediation of vanadium from marine environment and value-addition using potential thraustochytrids. BIORESOURCE TECHNOLOGY 2024:131356. [PMID: 39186987 DOI: 10.1016/j.biortech.2024.131356] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2024] [Revised: 08/24/2024] [Accepted: 08/24/2024] [Indexed: 08/28/2024]
Abstract
Rising concerns about global environmental degradation underscore the pressing need for effective solutions to combat heavy metal pollution. Industries such as semiconductor and steel production discharge vanadium into marine ecosystems, posing significant risks to both marine life and human health. The current study investigates efficacy of utilizing marine thraustochytrid for efficient vanadium removal outcompeting other microbial sources. By optimizing pH and temperature conditions during harvesting, achieved a remarkable 50.80 % enhancement in vanadium removal efficiency, from 19.31 to 29.12 mg/L. Furthermore, chelating agents EDTA and citric acid supplementation demonstrated promising enhancements, reaching up to 31.21 and 32.59 mg/L, respectively. Notably, vanadium-treated biomass supplemented with citric acid exhibited maximum enhancement in lipid content, from 58.47 to 75.34 %, indicating thraustochytrid's potential for biofuel production. This study presents a sustainable approach for industrial-scale vanadium bioremediation, aligning with Sustainable Development Goals focused on dual benefits of environmental protection and renewable energy.
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Affiliation(s)
- Ajeet Singh Chauhan
- Institute of Aquatic Science and Technology, College of Hydrosphere, National Kaohsiung University of Science and Technology, Kaohsiung City 81157, Taiwan
| | - Reeta Rani Singhania
- Institute of Aquatic Science and Technology, College of Hydrosphere, National Kaohsiung University of Science and Technology, Kaohsiung City 81157, Taiwan; Centre for Energy and Environmental Sustainability, Lucknow 226 029, Uttar Pradesh, India
| | - Anil Kumar Patel
- Institute of Aquatic Science and Technology, College of Hydrosphere, National Kaohsiung University of Science and Technology, Kaohsiung City 81157, Taiwan; Centre for Energy and Environmental Sustainability, Lucknow 226 029, Uttar Pradesh, India.
| | - Shashi Kant Bhatia
- Department of Biological Engineering, College of Engineering, Konkuk University, Seoul 05029, Republic of Korea
| | - Jo-Shu Chang
- Department of Chemical and Materials Engineering, Tunghai University, Taiwan; Research Center for Smart Sustainable Circular Economy, Tunghai University, Taiwan
| | - Chiu-Wen Chen
- Institute of Aquatic Science and Technology, College of Hydrosphere, National Kaohsiung University of Science and Technology, Kaohsiung City 81157, Taiwan; Department of Marine Environmental Engineering, National Kaohsiung University of Science and Technology, Kaohsiung City, Taiwan
| | - Cheng-Di Dong
- Institute of Aquatic Science and Technology, College of Hydrosphere, National Kaohsiung University of Science and Technology, Kaohsiung City 81157, Taiwan; Department of Marine Environmental Engineering, National Kaohsiung University of Science and Technology, Kaohsiung City, Taiwan.
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2
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Bakhshandeh A, Levin Y. On the Validity of Constant pH Simulations. J Chem Theory Comput 2024; 20:1889-1896. [PMID: 38359410 DOI: 10.1021/acs.jctc.3c01360] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/17/2024]
Abstract
Constant pH (cpH) simulations are now a standard tool for investigating charge regulation in coarse-grained models of polyelectrolytes and colloidal systems. Originally developed for studying solutions with implicit ions, extending this method to systems with explicit ions or solvents presents several challenges. Ensuring proper charge neutrality within the simulation cell requires performing titration moves in sync with the insertion or deletion of ions, a crucial aspect often overlooked in the literature. Contrary to the prevailing views, cpH simulations are inherently grand-canonical, meaning that the controlled pH is that of the reservoir. The presence of the Donnan potential between the implicit reservoir and the simulation cell introduces significant differences between titration curves calculated for open and closed systems; the pH of an isolated (closed) system is different from the pH of the reservoir for the same protonation state of the polyelectrolyte. To underscore this point, in this paper, we will compare the titration curves calculated using the usual cpH algorithm with those from the exact canonical simulation algorithm. In the latter case, titration moves adhere to the correct detailed balance condition, and pH is calculated using the recently introduced surface Widom insertion algorithm. Our findings reveal a very significant difference between the titration isotherms obtained using the standard cpH algorithm and the canonical titration algorithm, emphasizing the importance of using the correct simulation approach when studying charge regulation of polyelectrolytes, proteins, and colloidal particles.
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Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa P.O. Box 15051, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa P.O. Box 15051, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
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3
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López-Flores L, de la Cruz MO. Induced phase transformation in ionizable colloidal nanoparticles. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:122. [PMID: 38060163 PMCID: PMC10703989 DOI: 10.1140/epje/s10189-023-00386-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2023] [Accepted: 11/22/2023] [Indexed: 12/08/2023]
Abstract
Acid-base equilibria directly influence the functionality and behavior of particles in a system. Due to the ionizing effects of acid-base functional groups, particles will undergo charge exchange. The degree of ionization and their intermolecular and electrostatic interactions are controlled by varying the pH and salt concentration of the solution in a system. Although the pH can be tuned in experiments, it is hard to model this effect using simulations or theoretical approaches. This is due to the difficulty in treating charge regulation and capturing the cooperative effects in a colloidal suspension with Coulombic interaction. In this work, we analyze a suspension of ionizable colloidal particles via molecular dynamics (MD) simulations, along with Monte Carlo simulations for charge regulation (MC-CR) and derive a phase diagram of the system as a function of pH. It is observed that as pH increases, particles functionalized with acid groups change their arrangement from face-centered cubic (FCC) packing to a disordered state. We attribute these transitions to an increase in the degree of charge polydispersity arising from an increase in pH. Our work shows that charge regulation leads to amorphous solids in colloids when the mean nanoparticle charge is sufficiently high.
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Affiliation(s)
- Leticia López-Flores
- Department of Materials Science and Engineering, Northwestern University, Evanston, IL, 60208, USA
| | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering, Northwestern University, Evanston, IL, 60208, USA.
- Department of Chemistry, Northwestern University, Evanston, IL, 60208, USA.
- Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA.
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4
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Li Y, Kim M, Pial TH, Lin Y, Cui H, Olvera de la Cruz M. Aggregation-Induced Asymmetric Charge States of Amino Acids in Supramolecular Nanofibers. J Phys Chem B 2023; 127:8176-8184. [PMID: 37721979 DOI: 10.1021/acs.jpcb.3c05598] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/20/2023]
Abstract
Electrostatic interactions contribute critically to the kinetic pathways and thermodynamic outcomes of peptide self-assembly involving one or more than one charged amino acids. While it is well understood in protein folding that those amino acids with acidic/basic side chains could shift their pKas when placed in a hydrophobic microenvironment, to what extent aggregation of monomeric peptide units from the bulk solution could alter their charged status and how this change in pKa values would reciprocally impact their assembly outcomes. Here, we design and analyze two solution systems containing peptide amphiphiles with hydrocarbon chains of different lengths to determine the factor of deprotonation on assembly. Our results suggest that models of supramolecular nanofibers with uniformly distributed, fully charged amino acids are oversimplified. We demonstrate, with molecular dynamics simulations, and validate with experimental results that asymmetric, different protonation states of the peptides lead to distinct nanostructures after self-assembly. The results give estimates on the electrostatic interactions in peptide amphiphiles required for their self-assembly and shed light on modeling molecular assembly systems containing charged amino acids.
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Affiliation(s)
- Y Li
- Department of Chemical and Biomolecular Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
- Center of Computation and Theory of Soft Materials, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - M Kim
- Department of Chemical and Biomolecular Engineering and Institute for NanoBiotechnology, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, United States
| | - T H Pial
- Center of Computation and Theory of Soft Materials, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
- Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, Illinois 60208, United States
| | - Y Lin
- Center of Computation and Theory of Soft Materials, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - H Cui
- Department of Chemical and Biomolecular Engineering and Institute for NanoBiotechnology, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, United States
- Department of Oncology and Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205, United States
| | - M Olvera de la Cruz
- Department of Chemical and Biomolecular Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
- Center of Computation and Theory of Soft Materials, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
- Department of Materials Science and Engineering, Northwestern University, 2220 Campus Drive, Evanston, Illinois 60208, United States
- Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
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5
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Levin Y, Bakhshandeh A. A new method for reactive constant pH simulations. J Chem Phys 2023; 159:111101. [PMID: 37721322 DOI: 10.1063/5.0166840] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 08/29/2023] [Indexed: 09/19/2023] Open
Abstract
We present a simulation method that allows us to calculate the titration curves for systems undergoing protonation/deprotonation reactions-such as charged colloidal suspensions with acidic/basic surface groups, polyelectrolytes, polyampholytes, and proteins. The new approach allows us to simultaneously obtain titration curves both for systems in contact with salt and acid reservoir (semi-grand canonical ensemble) and for isolated suspensions (canonical ensemble). To treat the electrostatic interactions, we present a new method based on Ewald summation-which accounts for the existence of both Bethe and Donnan potentials within the simulation cell. We show that the Donnan potential dramatically affects the pH of a suspension. Counterintuitively, we find that in suspensions with a large volume fraction of nanoparticles and low ionic strength, the number of deprotonated groups can be 100% larger in an isolated system, compared to a system connected to a reservoir by a semi-permeable membrane-both systems being at exactly the same pH.
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Affiliation(s)
- Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
| | - Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
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6
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Wang J, Waltmann C, Harms C, Hu S, Hegarty J, Shindel B, Wang Q, Dravid V, Shull KR, Torkelson JM, Olvera de la Cruz M. Tailoring Interactions of Random Copolymer Polyelectrolyte Complexes to Remove Nanoplastic Contaminants from Water. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:7514-7523. [PMID: 37196238 DOI: 10.1021/acs.langmuir.3c01028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
We investigate the usage of polyelectrolyte complex materials for water remediation purposes, specifically their ability to remove nanoplastics from water, on which there is currently little to no prior research. We demonstrate that oppositely charged random copolymers are effective at quantitatively removing nanoplastic contamination from aqueous solution. The mechanisms underlying this remediation ability are explored through computational simulations, with corroborating quartz crystal microbalance adsorption experiments. We find that hydrophobic nanostructures and interactions likely play an important role.
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Affiliation(s)
- Jeremy Wang
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Curt Waltmann
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Caroline Harms
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Sumeng Hu
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - John Hegarty
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Benjamin Shindel
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Qifeng Wang
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Vinayak Dravid
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Kenneth R Shull
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - John M Torkelson
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, United States
| | - Monica Olvera de la Cruz
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
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7
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Qin S, Nap RJ, Huang K, Szleifer I. Influence of Membrane Permittivity on Charge Regulation of Weak Polyelectrolytes End-Tethered in Nanopores. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Shiyi Qin
- Department of Biomedical Engineering, Northwestern University, Evanston, Illinois 60208, United States
- Chemistry of Life Processes Institute, Northwestern University, Evanston, Illinois 60208, United States
| | - Rikkert J. Nap
- Department of Biomedical Engineering, Northwestern University, Evanston, Illinois 60208, United States
- Chemistry of Life Processes Institute, Northwestern University, Evanston, Illinois 60208, United States
| | - Kai Huang
- Institute of Systems and Physical Biology, Shenzhen Bay Laboratory, Shenzhen 518107, China
| | - Igal Szleifer
- Department of Biomedical Engineering, Northwestern University, Evanston, Illinois 60208, United States
- Chemistry of Life Processes Institute, Northwestern University, Evanston, Illinois 60208, United States
- Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States
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8
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Curk T, Yuan J, Luijten E. Accelerated simulation method for charge regulation effects. J Chem Phys 2022; 156:044122. [PMID: 35105090 DOI: 10.1063/5.0066432] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, charge regulation (CR), in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient CR Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the large-scale Atomic/Molecular Massively Parallel Simulator molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of CR on the nature of the polyelectrolyte coil-globule transition and on the effective interaction between oppositely charged nanoparticles.
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Affiliation(s)
- Tine Curk
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
| | - Jiaxing Yuan
- School of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Erik Luijten
- Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA
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9
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Bakhshandeh A, Frydel D, Levin Y. Reactive Monte Carlo simulations for charge regulation of colloidal particles. J Chem Phys 2022; 156:014108. [PMID: 34998334 DOI: 10.1063/5.0077956] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
We use a reactive Monte Carlo simulation method and the primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different numbers of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium chloride, the titration curves are compared with the experimental measurements obtained using potentiometric titration. A good agreement is found between simulations and experiments. In the case of lithium chloride, the specific ionic adsorption is taken into account through the partial dehydration of lithium ion.
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Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
| | - Derek Frydel
- Department of Chemistry, Universidad Técnica Federico Santa María, Campus San Joaquin, 7820275 Santiago, Chile
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, RS, Brazil
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10
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Bakhshandeh A, Segala M, Escobar Colla T. Equilibrium Conformations and Surface Charge Regulation of Spherical Polymer Brushes in Stretched Regimes. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c02077] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
- Departamento de Físico-Química, Instituto de Química, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
| | - Maximiliano Segala
- Instituto de Física, Universidade Federal de Ouro Preto, 35400-000 Ouro Preto, Minas Gerais, Brazil
- Departamento de Físico-Química, Instituto de Química, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
| | - Thiago Escobar Colla
- Instituto de Física, Universidade Federal de Ouro Preto, 35400-000 Ouro Preto, Minas Gerais, Brazil
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11
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Knoerdel AR, Blocher McTigue WC, Sing CE. Transfer Matrix Model of pH Effects in Polymeric Complex Coacervation. J Phys Chem B 2021; 125:8965-8980. [PMID: 34328340 DOI: 10.1021/acs.jpcb.1c03065] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Oppositely charged polyelectrolytes can undergo an associative phase separation, in a process known as polymeric complex coacervation. This phenomenon is driven by the electrostatic attraction between polyanion and polycation species, leading to the formation of a polymer-dense coacervate phase and a coexisting polymer-dilute supernatant phase. There has been significant recent interest in the physical origin and features of coacervation; yet notably, experiments often use weak polyelectrolytes the charge state of which depends on solution pH, while theoretical or computational efforts typically assume strong polyelectrolytes that remain fully charged. There have been only a few efforts to address this limitation, and thus there has been little exploration of how pH can affect complex coacervation. In this paper, we modify a transfer matrix theory of coacervation to account for acid-base equilibria, taking advantage of its ability to directly account for some local ion correlations that will affect monomer charging. We show that coacervation can stabilize the charged state of a weak polyelectrolyte via the proximity of oppositely charged monomers, and can lead to asymmetric phase diagrams where the positively and negatively charged polyelectrolytes exhibit different behaviors near the pKa of either chain. Specifically, there is a partitioning of one of the salt species to a coacervate to maintain electroneutrality when one of the polyelectrolytes is only partially charged. This results in the depletion of the same salt species in the supernatant, and overall can suppress phase separation. We also demonstrate that, when one of the species is only partially charged, mixtures that are off-stoichiometric in volume fraction but stoichiometric in charge exhibit the greatest propensity to form coacervate phases.
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Affiliation(s)
- Ashley R Knoerdel
- Program in Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Whitney C Blocher McTigue
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Charles E Sing
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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12
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Ghasemi M, Larson RG. Role of electrostatic interactions in charge regulation of weakly dissociating polyacids. Prog Polym Sci 2021. [DOI: 10.1016/j.progpolymsci.2020.101322] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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13
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Bakhshandeh A, dos Santos AP, Levin Y. Interaction between Charge-Regulated Metal Nanoparticles in an Electrolyte Solution. J Phys Chem B 2020; 124:11762-11770. [DOI: 10.1021/acs.jpcb.0c09446] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
| | - Alexandre P. dos Santos
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil
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