Enrique González | Mathematical Physics | Best Researcher Award

Assist. Prof. Dr. Enrique González | Mathematical Physics | Best Researcher Award

Associate professor at National University of Córdoba, Argentina

Assist. Prof. Dr. Enrique Ramón González is a distinguished physicist specializing in nuclear physics, gamma spectrometry, Monte Carlo simulations, and radiation detection, with strong expertise in environmental radioactivity and material characterization. He earned his Ph.D. in Physics from the National University of Córdoba and currently serves as Assistant Professor at FAMAF, where he actively combines research and teaching. His scholarly contributions include numerous publications in reputed journals such as Applied Radiation and Isotopes and Journal of Materials Science Research and Reviews, alongside presentations at leading international and national scientific meetings. Dr. González has participated in several research projects with a focus on environmental monitoring and advanced methods in radiation studies, demonstrating his commitment to both academic excellence and societal impact. His ongoing work reflects a balance of innovation, collaboration, and leadership in the scientific community.

Professional Profile

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Education

Assist. Prof. Dr. Enrique Ramón González pursued his academic path in physics with dedication and excellence. He completed his Licentiate Degree in Physics at the Faculty of Mathematics, Astronomy, Physics and Computing (FAMAF), National University of Córdoba, where he later obtained his Ph.D. in Physics with research focused on radiation detection, gamma spectrometry, and Monte Carlo simulations. His education provided him with a solid foundation in nuclear physics, experimental techniques, and computational methods, equipping him to address complex scientific problems. Throughout his academic journey, he has consistently demonstrated a balance between theoretical understanding and practical application. His advanced training not only strengthened his expertise in radiation and environmental physics but also prepared him to become a mentor, researcher, and educator within the global scientific community.

Experience

Dr. Enrique González has accumulated extensive academic and research experience across teaching, collaborative projects, and scientific presentations. He has served as a teaching assistant and later as Assistant Professor at the National University of Córdoba, where he has taught core physics subjects such as General Physics, Modern Physics, and specialized courses on radiation interaction with matter. Beyond his teaching, he has played an important role in research groups working on environmental radioactivity, material characterization, and nuclear spectroscopy, contributing to both national and international projects. His experience includes presenting at numerous scientific congresses, symposia, and meetings of the Argentine Physics Association, where he has shared innovative research findings. This combination of academic teaching, research activity, and professional collaborations highlights his well-rounded contribution to physics and education.

Research Interest

Dr. González’s research interests are centered on nuclear physics, gamma spectrometry, and the application of Monte Carlo simulations in radiation detection and measurement. He focuses on advancing methods for the analysis of radioactive spectra, gamma coincidence studies, and the determination of naturally occurring radioactivity in environmental samples. His work also extends to the study of radiation transport, detector calibration, and metrology of radionuclides, addressing both theoretical frameworks and experimental designs. A strong area of interest is environmental radioactivity, particularly in evaluating soil, food, and water samples for radiation levels, supporting sustainable practices and public safety. Additionally, he explores advanced material characterization through spectroscopy and computational modeling, demonstrating a deep interest in connecting fundamental research with practical applications for society and environmental care.

Awards and Honors

Dr. Enrique González has gained recognition within the scientific community through his impactful research contributions, peer-reviewed publications, and active involvement in international symposia and academic meetings. His participation in awarded projects such as environmental monitoring and advanced radiation analysis reflects the value and credibility of his research. These collaborative projects, supported by academic institutions, underline his role in addressing critical scientific and environmental challenges. His work published in reputed journals, including Applied Radiation and Isotopes, stands as a testament to his scholarly excellence and technical innovation. The honors associated with his contributions highlight his ability to integrate theory with applied science, creating a meaningful impact on both academia and society. His career achievements position him as a respected figure in nuclear and radiation physics.

Research Skill

Dr. González possesses a wide range of advanced research skills in the field of nuclear and radiation physics. He is proficient in gamma spectrometry, Monte Carlo simulations for radiation transport, detector calibration, and analysis of complex radioactive spectra. His expertise includes working with simulation codes such as PENELOPE and MCNP5, alongside programming knowledge in Fortran and Python for scientific modeling. Skilled in data analysis and computational methods, he integrates theoretical models with experimental designs to achieve accurate results. He also demonstrates expertise in spectroscopic techniques applied to both environmental and material science research. His skills extend to academic writing, conference presentations, and collaboration in multidisciplinary projects. This versatile skill set highlights his ability to adapt, innovate, and contribute significantly to scientific advancements and applied research.

Publication Top Notes

  • Title: A DFT study of ZnO, Al2O3 and SiO2; combining X-ray spectroscopy, chemical bonding and Wannier functions
    Authors: GB Grad, ER González, J Torres-Díaz, EV Bonzi
    Year: 2022
    Citation: 12

  • Title: A methodology to determine natural radioactivity by γ spectrometry without using calibrated standard samples
    Authors: ER González, RT Mainardi, GB Grad, EV Bonzi
    Year: 2017
    Citation: 4

  • Title: Influence of the sample density in γ spectrometry
    Authors: ER González, GB Grad, EV Bonzi
    Year: 2019
    Citation: 2

  • Title: Analysis of electronic structure and X-ray absorption and emission spectra in MgO within the FP-LAPW method
    Authors: GB Grad, E González, J Torres Díaz, E Bonzi
    Year: 2018
    Citation: 2

  • Title: Determinación de K-40 en alimentos por espectrometría gamma con un detector de NaI (Tl) y simulaciones Monte Carlo
    Authors: ER González, EV Bonzi
    Year: 2012
    Citation: 1

  • Title: Determination of the coincidence summing gamma spectrum of a 60Co source by Monte Carlo simulations taking into account the angular correlation γ-γ
    Authors: ER González
    Year: 2025

  • Title: Desarrollo de un método basado en simulación Monte Carlo para el cálculo y análisis de espectros gamma complejos, sin el uso de fuentes de referencia
    Authors: ER González
    Year: 2019

  • Title: Determination of K-40 in foods by gamma spectrometry with a NaI (Tl) detector and Monte Carlo simulations
    Authors: ER González, EV Bonzi
    Year: 2011

  • Title: Analytical and Monte Carlo calculations of the radiation emitted from a cylindrical radioactive sample
    Authors: RT Mainardi, ER González, EV Bonzi
    Year: 2007

Conclusion

Assist. Prof. Dr. Enrique Ramón González exemplifies the qualities of a dedicated researcher, teacher, and innovator in nuclear physics and radiation studies. His career reflects a balance of academic teaching, research productivity, and international collaboration, making him a valuable contributor to both science and society. His expertise in gamma spectrometry, Monte Carlo simulations, and environmental radioactivity has led to meaningful advancements in the field, while his participation in research projects demonstrates his commitment to addressing global challenges. With a strong publication record, consistent conference engagement, and leadership in collaborative studies, Dr. González stands out as a researcher who bridges theory and practice. His future potential lies in expanding international partnerships, publishing in leading journals, and continuing to mentor the next generation of physicists.

lhtisham ul haq | Mathematical Physics | Best Researcher Award

Dr. lhtisham ul haq | Mathematical Physics | Best Researcher Award

Student at University of Science and Technology China, China

Dr. Ihtisham Ulhaq is an emerging physicist and sustainability innovator 🌱🔬, currently advancing his Ph.D. at the University of Science and Technology of China 🇨🇳. With a robust foundation in materials science and renewable energy, his pioneering research on lead-free perovskite solar cells ⚡ and spectrally split agrivoltaic systems 🌞🌾 is shaping eco-friendly energy solutions with global relevance. Dr. Ulhaq has authored 12 peer-reviewed publications 📚—five as the lead author—across high-impact Q1/Q2 journals, showcasing his scientific rigor and thought leadership. His multidisciplinary collaborations across China, Saudi Arabia, and Pakistan foster cutting-edge innovation in nanomaterials, photovoltaics, and sustainable agriculture 🤝🌍. With hands-on expertise in MOCVD, thin-film deposition, and doping strategies, he is bridging theoretical insights with scalable applications. Passionate, visionary, and globally connected, Dr. Ulhaq is driving transformative change in the fields of clean energy and agritech, embodying the spirit of next-generation research excellence 🌐🏆.

Professional Profile

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Education 🎓📚

Dr. Ihtisham Ulhaq’s academic journey reflects a deep commitment to the frontiers of physics and sustainable technologies. He earned his M.Phil. in Physics from the University of Lahore 🇵🇰, where he laid the groundwork for his specialization in energy materials. Currently pursuing his Ph.D. at the prestigious University of Science and Technology of China 🇨🇳, Dr. Ulhaq focuses on renewable energy and advanced materials research. His educational background is anchored in strong theoretical physics, coupled with a practical mastery of experimental tools such as thin-film deposition, nanostructuring, and semiconductor engineering 🔬. With a curriculum steeped in interdisciplinary learning and international exposure, he has cultivated the analytical and innovative skill set required to solve global energy and environmental challenges 🌍. His academic excellence has been consistently demonstrated through scholarly achievements, publication output, and research-led learning, laying a solid foundation for a promising career in advanced scientific innovation 🌟.

Professional Experience 🧪🏢

Though still early in his career, Dr. Ihtisham Ulhaq has amassed significant professional experience through intensive academic research and collaborative projects. As a doctoral researcher at the University of Science and Technology of China, he has spearheaded studies in photovoltaics, nanomaterials, and solar cell optimization ☀️. He has independently led and co-led three major research initiatives, including the design of a spectrally split agrivoltaic system combined with container farming 🌿🏗️—a novel concept integrating agriculture and energy efficiency. His work environment emphasizes international collaboration, where he has actively engaged with research partners across China, Saudi Arabia, and Pakistan 🤝. His hands-on experience in laboratory techniques such as MOCVD, doping analysis, and electron transport layer enhancement equips him with a comprehensive skill set ideal for next-gen green technologies 💡. Dr. Ulhaq’s professional path is defined by rigorous experimentation, innovation-oriented thinking, and a mission to translate science into sustainable global solutions 🌐.

Research Interest 🔍⚡

Dr. Ihtisham Ulhaq’s research passion lies at the intersection of clean energy, nanotechnology, and sustainable agriculture. He specializes in developing lead-free perovskite solar cells, aiming to improve their stability, efficiency, and environmental safety 🌞♻️. His interest extends to agrivoltaics, where he designs hybrid systems combining renewable energy generation with agricultural productivity—an area where he proposed a unique spectrally split system for container farming 🌾💧. His scientific curiosity drives explorations in bandgap engineering, doping strategies, and interface tailoring to enhance energy material performance at the nanoscale. He is equally intrigued by the optical and magnetic properties of functional thin films, especially ferrite-based materials with communication applications 📡. With a vision to create integrated, eco-friendly technologies, Dr. Ulhaq’s research is highly interdisciplinary and aligned with sustainable development goals 🧭. He is deeply committed to transforming lab-scale discoveries into scalable, real-world solutions that contribute to a greener and more resilient future 🌍🔋.

Awards and Honors 🏆🎖️

While still in the formative years of his research career, Dr. Ihtisham Ulhaq’s accomplishments have earned him increasing recognition in academic circles 🌟. His 12 peer-reviewed journal publications, five of which he authored as the primary investigator, have appeared in reputable Q1/Q2 scientific journals—a significant feat in competitive research domains 📘🧠. His work on lead-free perovskite solar cells and agrivoltaic systems has garnered attention for its originality and relevance to sustainable innovation 🌱🔬. While he is actively being considered for prominent awards such as the Best Researcher Award, his contributions are already making ripples within the scientific community through impactful research and global collaboration 🌐. As a rising researcher, he is paving the way for future distinctions, honors, and fellowships tied to innovation, green energy, and interdisciplinary science. These early milestones reflect a trajectory of excellence, driven by purpose, persistence, and a profound scientific vision 🧭.

Conclusion ✨📈

Dr. Ihtisham Ulhaq exemplifies the spirit of the modern researcher: globally engaged, scientifically rigorous, and deeply committed to sustainability. Through his pioneering work in clean energy—particularly in lead-free perovskite solar cells and agrivoltaic system integration—he is addressing some of the most urgent challenges of our time 🌍⚡. His multidisciplinary expertise, spanning materials science, physics, nanotechnology, and agriculture, positions him as a key innovator in eco-technology and renewable solutions 🔄🌿. With a growing publication record, dynamic collaborations, and a proactive approach to scientific inquiry, Dr. Ulhaq is not only building a distinguished academic profile but also laying the groundwork for real-world impact 🏗️📊. As he continues to expand his research, leadership, and outreach, his trajectory promises contributions that will resonate globally. In every dimension—academic, practical, and visionary—Dr. Ulhaq embodies the values deserving of recognition through the Best Researcher Award 🏅.

Publications Top Notes

🔬 Title: Impact of molybdenum doping on the optoelectronic and structural properties of CsPbIBr₂ perovskite solar cell
👨‍🔬 Authors: MI Khan, A Mujtaba, S Hussain, M Atif, AI Qureshi, W Shahid, A Ali
📅 Year: 2024
📈 Citations: 29
📚 Source: Physica B: Condensed Matter, Volume 678, Article 415758


🔬 Title: Bandgap reduction and efficiency enhancement in Cs₂AgBiBr₆ double perovskite solar cells through gallium substitution
👨‍🔬 Authors: MI Khan, A Ullah, A Mujtaba, BS Almutairi, W Shahid, A Ali, JR Choi
📅 Year: 2024
📈 Citations: 24
📚 Source: RSC Advances, Volume 14 (8), Pages 5440–5448


🔬 Title: Influence of gallium on structural, optical and magnetic properties of Bi-YIG thin films
👨‍🔬 Authors: MS Hasan, MI Khan, SS Ali, A Brahmia
📅 Year: 2024
📈 Citations: 10
📚 Source: Materials Science and Engineering: B, Volume 301, Article 117180


🔬 Title: Bandgap Engineering and Enhancing Optoelectronic Performance of a Lead-Free Double Perovskite Cs₂AgBiBr₆ Solar Cell via Al Doping
👨‍🔬 Authors: A Ullah, M Iftikhar Khan, Ihtisham-ul-haq, BS Almutairi, DB N. AlResheedi, et al.
📅 Year: 2024
📈 Citations: 9
📚 Source: ACS Omega, Volume 9 (16), Pages 18202–18211


🔬 Title: Trans-polyacetylene doped Cs₂AgBiBr₆: Band gap reduction for high-efficiency lead-free double perovskite solar cells
👨‍🔬 Authors: A Ullah, MI Khan, BS Almutairi, A Laref, A Dahshan
📅 Year: 2024
📈 Citations: 4
📚 Source: Results in Physics, Volume 60, Article 107654


🔬 Title: A novel heterostructure of Cr-doped TiO₂ for reducing the recombination rate of dye sensitized solar cells
👨‍🔬 Authors: MI Yasin, MI Khan, S Kanwal, DBN ALResheedi, M Fatima, N Alwadai, et al.
📅 Year: 2024
📈 Citations: 3
📚 Source: Journal of the Korean Ceramic Society, Volume 61 (4), Pages 569–580


🔬 Title: Improving Cs₂AgBiBr₆ double perovskite solar cells through graphdiyne doping: A Stride towards enhanced performance
👨‍🔬 Authors: S Umer, MI Khan, A Ullah, M Asad, W Mnif, Z Algarni, MI Saleem
📅 Year: 2024
📈 Citations: 2
📚 Source: Optical Materials, Volume 156, Article 115896


🔬 Title: Roadmap to 2D Graphene Nanomaterials-Based Biosensors for Early Cancer Detection
👨‍🔬 Authors: JWLHIUHMA Khan
📅 Year: 2025
📈 Citations: 1
📚 Source: Plasmonics


🔬 Title: Enhancing efficiency in double perovskite solar cells through bandgap reduction via organic polymer doping
👨‍🔬 Authors: MI Khan, A Mujtaba, A Ullah, B Ali, M Atif, MS Hasan
📅 Year: 2025
📈 Citations: 1
📚 Source: Results in Chemistry, Volume 13, Article 101999


🔬 Title: Enhancing the Efficiency and Stability of Cs₂AgBiBr₆ Solar Cells via MAPbBr₃ Decoration
👨‍🔬 Authors: MI Khan, M Li, OAA Ali, SF Mahmoud
📅 Year: 2025
📚 Source: Materials Research Bulletin, Article 113501


🔬 Title: Enhancing efficiency of Cs₂AgBiBr₆ double perovskite solar cells through bandgap reduction by molybdenum doping
👨‍🔬 Authors: IMIKLBFHERP Patil
📅 Year: 2025
📚 Source: Journal of the Korean Ceramic Society


🔬 Title: Enhancing solar cell efficiency: lead-free double perovskite solar cells Cs₂AgBiBr₆ with magnesium-doped and Zn₂SnO₄ electron transport layer
👨‍🔬 Authors: MI Khan, Lamia Ben Farhat
📅 Year: 2024
📚 Source: Journal of Sol-Gel Science and Technology, Volume 112 (2), Pages 468–479

Zoriana Danel | Mathematical Physics | Best Researcher Award

Assoc. Prof. Dr. Zoriana Danel | Mathematical Physics | Best Researcher Award

WIMiF at Cracow University of Technology, Poland

Dr. Zoriana Danel (formerly Zoryana Usatenko) is an accomplished physicist with a distinguished career in theoretical and condensed matter physics. Born in Lviv in 1968, she earned her Ph.D. in Physics and Mathematics from the Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine and later completed her habilitation at Jagiellonian University in Poland. Currently an Associate Professor with Habilitation at the Faculty of Materials Engineering and Physics, Cracow University of Technology, she has an extensive background in soft matter physics, polymer physics, statistical physics, and biophysics. Dr. Danel has held numerous prestigious international fellowships, including from the von Humboldt Foundation and DAAD, and has contributed to various international research collaborations. A prolific speaker and author, she has presented at major conferences across Europe and Asia and published extensively. Fluent in multiple languages, she is also actively engaged in academic supervision and peer review.

Professional Profile 

Scopus Profile
ORCID Profile

Education

Dr. Zoriana Danel began her academic journey in physics with a strong foundation in Lviv, Ukraine. She obtained her Ph.D. in Physics and Mathematics in 1996 from the Institute for Condensed Matter Physics at the National Academy of Sciences of Ukraine, under the mentorship of Prof. I.V. Stasyuk. Her doctoral research focused on statistical theories related to condensed matter systems. Recognizing her growing expertise, she pursued and successfully completed her Habilitation (D.Sc.) in 2014 at the Jagiellonian University in Kraków, Poland, further solidifying her academic authority in theoretical and condensed matter physics. Her postdoctoral development included prestigious fellowships in Germany, enabling her to work under top international scholars and expand her research network. With a strong academic background shaped by institutions known for their scientific rigor, Dr. Danel has built an interdisciplinary and globally informed scientific profile, seamlessly integrating education, research, and international collaboration throughout her academic evolution.

Professional Experience

Dr. Zoriana Danel has accumulated a wealth of professional experience across esteemed institutions in Ukraine, Poland, and Germany. Early in her career, she contributed as a researcher at the Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, where she honed her skills in statistical physics and soft matter theory. Following her habilitation, she joined the Faculty of Materials Engineering and Physics at the Cracow University of Technology in Poland, where she currently serves as an Associate Professor with Habilitation. Her academic duties include supervising master’s and doctoral theses, mentoring early-career researchers, and developing physics curricula. Dr. Danel has also held prestigious research fellowships and visiting professorships in institutions across Germany, including positions supported by the Alexander von Humboldt Foundation and the DAAD. Through her roles in academia and international research, she has consistently bridged theoretical development with practical applications, cultivating an impactful and respected academic career.

Research Interest

Dr. Zoriana Danel’s research interests are both broad and deeply specialized, reflecting her expertise in theoretical physics and her interdisciplinary approach. She focuses primarily on soft matter physics, polymer physics, and statistical physics, with particular emphasis on the theoretical modeling of complex systems. Her studies often address the behavior of polymers in disordered environments, confined geometries, and the influence of fractal structures on macromolecular dynamics. She also engages in biophysical research, examining biological polymers and their interaction with cellular structures. Using tools from statistical mechanics and field theory, Dr. Danel investigates how environmental constraints and topological factors affect the behavior of macromolecules, such as DNA and synthetic polymers. Her work contributes significantly to understanding nanoscale phenomena and the physics of self-organization. By connecting theoretical insights to experimental observations, she has fostered collaborations with material scientists, chemists, and biophysicists, thereby advancing interdisciplinary research with potential applications in nanotechnology and biotechnology.

Award and Honor

Throughout her career, Dr. Zoriana Danel has been the recipient of numerous prestigious awards and fellowships that underscore her international recognition and scientific excellence. Most notably, she has received a fellowship from the Alexander von Humboldt Foundation in Germany, a testament to the global impact of her research in physics. She has also been a recipient of multiple DAAD fellowships, which supported her scientific work at German institutions and fostered valuable international collaboration. In addition, Dr. Danel was selected as a visiting researcher at top-tier German universities, such as the Technical University of Munich and Heinrich Heine University Düsseldorf. Her contributions to theoretical physics and interdisciplinary studies have consistently been acknowledged through invitations to present at international conferences and by peer-reviewed journals where she serves as a reviewer. These accolades reflect her sustained excellence in research, her dedication to scientific progress, and her leadership within the international academic community.

Conclusion

Dr. Zoriana Danel is a distinguished physicist whose career exemplifies academic rigor, international collaboration, and scientific innovation. With a strong foundation in theoretical and condensed matter physics, she has expanded her expertise into soft matter, biophysics, and interdisciplinary research. Her educational journey, marked by a Ph.D. from Ukraine and habilitation in Poland, and professional engagements across leading European institutions, highlight her adaptability and influence. Through her pioneering research on polymers in complex environments and her contributions to statistical physics, she continues to push the boundaries of modern theoretical understanding. Dr. Danel’s accolades, including the Humboldt and DAAD fellowships, further affirm her global standing. Beyond her research, she is a dedicated educator and mentor, shaping the next generation of physicists. Her career is a model of how scientific curiosity, rigorous scholarship, and international engagement can converge to make a lasting impact in both academia and applied science.

Publications Top Notes

  • Title: Analytical and Numerical Investigation of Star Polymers in Confined Geometries
    Authors: Zoriana Danel, Joanna Halun, Paweł Karbowniczek
    Year: 2024
    Source: International Journal of Molecular Sciences
    DOI: 10.3390/ijms25179561

  • Title: Entropic Force in a Dilute Solution of Real Ring Polymer Chains with Different Topological Structures in a Slit of Two Parallel Walls with Mixed Boundary Conditions
    Authors: Piotr Kuterba, Zoriana Danel, Wolfhard Janke
    Year: 2023
    Source: Condensed Matter Physics
    DOI: 10.5488/cmp.26.43605

  • Title: Molecular Dynamics Simulations of the Monomer Density Profiles of Knotted Ring Polymer Chains Confined in a Slit of Two Parallel Walls with One Attractive and Another Repulsive Surface
    Authors: P. Kuterba, H. Christiansen, Z. Danel, W. Janke
    Year: 2023
    Source: Journal of Physics: Conference Series
    DOI: 10.1088/1742-6596/2436/1/012031

  • Title: Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations
    Authors: Zoriana Danel
    Year: 2021
    Source: Entropy
    DOI: 10.3390/e23020242

  • Title: Photoelectrical Properties and Surface Examination of Luminescent Copolymer Compounds
    Authors: Zoriana Danel
    Year: 2020
    Source: Applied Surface Science
    DOI: 10.1016/j.apsusc.2020.147366

  • Title: Investigations of the Optical and Thermal Properties of the Pyrazoloquinoline Derivatives and Their Application for OLED Design
    Authors: Zoriana Danel
    Year: 2020
    Source: Polymers
    DOI: 10.3390/polym12112707

  • Title: Corrigendum to “Monomer Density Profiles of Real Polymer Chains in Confined Geometries”
    Authors: Zoriana Danel
    Year: 2020
    Source: Journal of Molecular Liquids
    DOI: 10.1016/j.molliq.2019.112066

  • Title: Erratum: “Monomer Density Profiles for Polymer Chains in Confined Geometries: Massive Field Theory Approach”
    Authors: Zoriana Danel
    Year: 2019
    Source: The Journal of Chemical Physics
    DOI: 10.1063/1.5120038

  • Title: Ring Polymer Chains Confined in a Slit Geometry of Two Parallel Walls: The Massive Field Theory Approach
    Authors: Zoriana Danel
    Year: 2017
    Source: Journal of Statistical Mechanics: Theory and Experiment
    DOI: 10.1088/1742-5468/aa5285

  • Title: Polymer Chains in Confined Geometries: Massive Field Theory Approach
    Authors: Zoriana Danel
    Year: 2009
    Source: Physical Review E
    DOI: 10.1103/physreve.80.041802