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- ItemAccurate Laboratory Wavelengths of the A1Π(υ' = 0-5)-X1Σ+(υ'' = 0) Vibronic Bands of 12C17O and 12C18O(IOP Science, 2006) Du Plessis, Anton; Rohwer, Erich G.; Steenkamp, Christine M.
Show more Twenty nine rovibronic lines of 12C17O for which laboratory wavelengths were previously unavailable were detected in laser-induced fluorescence excitation spectra of the six vibronic bands A1Π(υ' = 0-5)-X1Σ+(υ'' = 0). Rovibronic lines of 12C16O, 13 C16O, 12C17O, and 12C 18O were detected in each band, allowing accurate determination of the unknown wavelengths using neighboring 12C16O and 13C16O lines as reference. The new wavelength data yield consistent heliocentric velocity values when applied to vacuum ultraviolet observations of 12C17O and 12C 18O in the interstellar medium.Show more - ItemAccurate laboratory wavelengths of the e 3 Σ–(ν' = 5) – X 1 Σ+(ν'' = 0) band of 12C16O(IOP Science, 2010) Dickenson, G. D.; Nortje, A. C.; Steenkamp, C. M.; Rohwer, E. G.; Du Plessis, A.
Show more The forbidden singlet-triplet transitions of carbon monoxide (CO) are important in the interpretation of vacuum ultraviolet interstellar absorption spectra and in particular for the measurement of large CO column densities. Twenty rovibronic lines of the e 3Σ–(ν' = 5) – X 1Σ+(ν'' = 0) band of 12 C 16O for which laboratory wavelengths were previously unavailable were identified in laser-induced fluorescence excitation spectra. Wavelengths were assigned to five rovibronic transitions to an average accuracy of 0.0028 Å. A further 15 lines could not be fully resolved and average wavelengths were measured for these groups of closely spaced lines. A wavelength difference of 0.011 ± 0.0028 Å between the measured wavelengths and the calculated wavelengths in the atlas of Eidelsberg & Rostas demonstrates the need for more experimental data on CO.Show more - ItemAccurate laboratory wavelengths of the vacuum ultraviolet A(v'=3)-X(v''=0) band of 12C17O and 12C18O(IOP Science, 2003) Steinmann, Christine M.; Rohwer, Erich G.; Stafast, Herbert
Show more Six individual rotational lines (J'' ≤ 3) of 12C17O, as well as four of 12C18O, were detected in the A 1Π(v' = 3)-X 1Σ+(v'' = 0) vibronic band, and their wavelengths determined using neighboring 12C16O and 13C16O lines as reference. The measurements (fluorescence excitation spectra) were performed in a pulsed supersonic jet (Ar or Ne as carrier gas) employing a tunable pulsed vacuum ultraviolet radiation source with a narrow bandwidth (~5 GHz). The new spectral data on 12C17O and 12C18O are applied to the interpretation of recent vacuum ultraviolet observations of 12C17O and 12C18O in the interstellar medium.Show more - ItemAdditional degrees of freedom associated with position measurements in non-commutative quantum mechanics(Stellenbosch : University of Stellenbosch, 2010-12) Rohwer, Christian M.; Scholtz, Frederik G.; University of Stellenbosch. Faculty of Science. Dept. of Physics.
Show more ENGLISH ABSTRACT: Due to the minimal length scale induced by non-commuting co-ordinates, it is not clear a priori what is meant by a position measurement on a non-commutative space. It was shown recently in a paper by Scholtz et al. that it is indeed possible to recover the notion of quantum mechanical position measurements consistently on the non-commutative plane. To do this, it is necessary to introduce weak (non-projective) measurements, formulated in terms of Positive Operator-Valued Measures (POVMs). In this thesis we shall demonstrate, however, that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the aforementioned formalism entails a description that is non-local in that it requires knowledge of all orders of positional derivatives through the star product that is used ubiquitously to map operator multiplication onto function multiplication in non-commutative systems. It will be shown that there exist several equivalent local descriptions, which are arrived at via the introduction of additional degrees of freedom. Consequently non-commutative quantum mechanical position measurements necessarily confront us with some additional structure which is necessary (in addition to position) to specify quantum states completely. The remainder of the thesis, based in part on a recent publication (\Noncommutative quantum mechanics { a perspective on structure and spatial extent", C.M. Rohwer, K.G. Zloshchastiev, L. Gouba and F.G. Scholtz, J. Phys. A: Math. Theor. 43 (2010) 345302) will involve investigations into the physical interpretation of these additional degrees of freedom. For one particular local formulation, the corresponding classical theory will be used to demonstrate that the concept of extended, structured objects emerges quite naturally and unavoidably there. This description will be shown to be equivalent to one describing a two-charge harmonically interacting composite in a strong magnetic eld found by Susskind. It will be argued through various applications that these notions also extend naturally to the quantum level, and constraints will be shown to arise there. A further local formulation will be introduced, where the natural interpretation is that of objects located at a point with a certain angular momentum about that point. This again enforces the idea of particles that are not point-like. Both local descriptions are convenient, in that they make explicit the additional structure which is encoded more subtly in the non-local description. Lastly we shall argue that the additional degrees of freedom introduced by local descriptions may also be thought of as gauge degrees of freedom in a gauge-invariant formulation of the theory.Show more - ItemAdvancing X-ray micro computed tomography in Africa : going far, together(Elsevier, 2019) Du Plessis, Anton; Le Roux, Stephan G.; Tshibalanganda, Muofhe
Show more X-ray micro computed tomography (microCT) is a high resolution non-destructive materials imaging technology and is emerging as a powerful tool for industrial and scientific research applications. The aim of this review paper is to present the capabilities and potential of this technique within an African context. This is done using a representative sample: all work done at the Stellenbosch CT facility during 2018 is used as an overview of the type of work done at such a facility in Africa. Besides the plethora of academic research topics, the most important industrial applications are also discussed, which assisted to keep the Stellenbosch CT facility financially operational. This provides a wider understanding of the opportunities and capabilities of this technique and how it can benefit African researchers and local industries. The question “what is it used for?”, and more specifically “what is it used for in Africa?” is therefore answered. The availability of such X-ray tomography facilities helps to fast-track research by providing local expertise and support in Africa for advancing African science. This model is not only applicable to microCT but applies to any collaborative scientific endeavor in Africa, with success rates depending on the efficient sharing of resources, providing expert skills and advancing African science in Africa. There is an African proverb “if you want to go fast – go alone; if you want to go far – go together”. Clearly, African science will go far by working together in such facilities.Show more - ItemAlpha cluster structure and scattering in 20Ne, 44Ti, 94Mo, 136Te and 212Po(Stellenbosch : University of Stellenbosch, 2011-03) Ndayishimye, Joram; Wyngaardt, Shaun M.; Perez, S. M.; University of Stellenbosch. Faculty of Science. Dept. of Physics.
Show more ENGLISH ABSTRACT: We investigate the nuclei 20Ne, 44Ti, 94Mo, 136Te and 212Po using a model of an α-cluster orbiting a closed shell core. A purely phenomenological cluster-core potential is found to provide a successful description of the spectra, B(E2↓) transition strengths, and α-decay rates of the low-lying positive parity states of these nuclei. We then use the same potential as the real part of an optical model potential to describe the α elastic scattering by 16O, 40Ca, 90Zr and 208Pb. The experimental differential cross-section data are reasonably well reproduced with the imaginary potential depth as the only free parameter. The special case of the 8Be system is also analysed.Show more - ItemAlpha-cluster structure in the ground state of 40Ca displayed in a (p,pa) knockout reaction(IOP Publishing, 2013) Cowley, A. A.
Show more The analyzing power is very sensitive to details of the reaction mechanism of (p, pα) knockout reactions in the incident energy range of approximately 100 MeV and higher. Whereas distorted wave impulse approximation calculations in the past proved to give an excellent reproduction of analyzing power angular distributions for quasifree (p, pα) reactions on light targets such as 6Li, 9Be and 12C, the situation for 40Ca was not as simple. It is now shown that the theory also offers good agreement with the experimental distribution of the heaviest target nucleus if care is taken to use proper distorted waves which treat α−36Ar properly as a system for which α–elastic scattering is anomalous. Thus it is shown that 40Ca reveals its ground state α–cluster structure in an unambiguous way similar to the light target nuclei.Show more - ItemAnalysis and applications of the generalised Dyson mapping(Stellenbosch : Stellenbosch University, 2004-12) Snyman, Izak; Geyer, H. B.; Scholtz, Frederik G.; Stellenbosch University. Faculty of Science. Dept. of Physics.
Show more ENGLISH ABSTRACT: In this thesis, generalized Dyson boson-fermion mappings are considered. These are techniques used in the analysis of the quantum many-body problem, and are instances of so-called boson expansion methods. A generalized Dyson boson-fermion mapping, or a Dyson mapping for short, is a one-to-one linear but non-unitary operator that can be applied to vectors representing the states of a many-fermion system. A vector representing a fermion system maps onto a vector that is most naturally interpreted as representing a state of a many-body system that contains both bosons and fermions. The motivation for doing such a mapping is the hope that the mapping will reveal some property of the system that simplifies its analysis and that was hidden in the original form. The aims of this thesis are 1. to review the theory of generalized Dyson boson-fermion mappings, 2. by considering a tutorial example, to demonstrate that it is feasible to implement the theory and 3. to find a useful application for a generalized Dyson boson-fermion mapping, by considering a non-trivial model, namely the Richardson model for superconductivity. The realization of the first two aims mainly involve the collecting together of ideas that have already appeared in the literature, into one coherent text. Some subtle points that were treated only briefly due to space restrictions in the journal publications where the theory was first expounded, are elaborated on in the present work. On the other hand, the analysis of the Richardson Hamiltonian that uses a Dyson mapping, goes beyond what has already appeared in the literature. It is the first time that a boson expansion technique is implemented for a system where the roles of both collective and non-collective fermion pairs are important. (The Dyson mapping associates bosons with Cooper pairs, while the fermions not bound in Cooper pairs result in fermions being present in the mapped system as well.) What is found is that the Dyson mapping uncovers non-trivial properties of the system. These properties aid the construction of time-independent perturbation expansions for the stationary states of the system, as well as time-dependent expansions for transition amplitudes between states. The time-independent expansions agree with results that other authors obtained through methods other than boson expansions. The time-dependent expansions, that one would be hard-pressed to develop without a Dyson mapping, might in future prove useful in understanding aspects of the dynamics of ultracold fermi gases, when time-dependent magnetic fields are used to vary the atom-atom interaction strenght.Show more - ItemThe analysis of multi-clustering in heavy nuclei(Stellenbosch : Stellenbosch University., 2020-04) Carolus, Timothy Gary; Wyngaardt, Shaun M.; Malaza, Vusi D.; Stellenbosch University. Faculty of Science. Dept. of Physics.
Show more ENGLISH ABSTRACT: The binary cluster model is the simplest mathematical model which is used to describe a system of strongly interacting, and highly correlated nuclear matter. This study will serve as a means to better understand the phenomenon of nuclear clustering beyond a 208P b-alpha cluster core system. Theoretically predicted observables, such as the cluster decay half-life, positive parity cluster states, and the reduced electric dipole transition (B(E2)) are compared to the available experimentally observed quantities. The results show that the tested systems for various cluster-core configurations, of both a fixed parent nuclei and fixed stable core favoured the phenomenological description of their interaction. A numerical optimization procedure is applied to the core- cluster potential of the binary cluster formalism and is then used as an analytical tool in order to predict the possibility of higher modes of cluster decay in 216Rn.Show more - ItemAnalyzing power and cross section distributions of the 12C (p,pα)8Be cluster knockout reaction at an incident energy of 100 MeV(Stellenbosch : University of Stellenbosch, 2010-03) Mabiala, Justin; Cowley, A. A.; Fortsch, S. V.; University of Stellenbosch. Faculty of Science. Dept. of Physics.
Show more ENGLISH ABSTRACT: The (p, pα) reaction on 12C was investigated experimentally using polarized incident protons of 100 MeV. Coincident data, which were obtained at ten quasifree angle pairs for proton angles ranging from 25◦ to 110◦, were analyzed in terms of the distorted-wave impulse approximation (DWIA). Calculated energy-sharing cross section and analyzing power distributions reproduce the data reasonably well. The observed agreement allows the extraction of distorted momentum distributions from experimental data. These distributions are very consistent over a wide range of angle pairs at which cross section energy-sharing distributions vary considerably. Since measurements of analyzing powers were made, spin-orbit distortions were included in the DWIA calculations. The effects of spin-orbit distortions were found to be very small near zero recoil momentum and did not destroy the validity of the factorization approximation where the two-body p-α cross section enters as a multiplicative factor in the three-body (p, pα) cross section expression. Spectroscopic factors derived from the data are fairly consistent with the trend of the theoretical predictions. Analyzing power data also follow the trend of free p-4He scattering data, and comparisons with DWIA predictions are in reasonable agreement. The theory reproduces also very well analyzing power angular distributions of the projectile-cluster two-body scattering at large angular momentum of the residual nucleus. This indicates that a quasifree knockout mechanism dominates the reaction. The two-body interaction response between the projectile and the α cluster was found to resemble the scattering of protons from a free α particle to a remarkable degree, the present results strongly imply the existence of preformed α clusters in 12C.Show more - ItemAngular correlation measurement with the iThemba LABS segmented clover detector(Jagellonian University, 2019) Shirinda, O.; Lawriea, E. A.; Buchera, T. D.; Mthembua, S. H.; Dinoko, T. R. S.; Easton, J. L.; Mtshali, W. X.; Noncolela, S. P.; Duprez, D.; Lawrie, J. J.
Show more Measurements of the angular correlation function W(θ) were performed with the iThemba LABS segmented clover detector. A set of measurements with radioactive sources and irradiated targets was carried out to check the performance of the detector. At short detector-to-source distance, the detector covers the whole range of angles needed for precise angular correlation measurements. Preliminary results show that our detector can measure precisely angular correlation functions, including for transitions with large multipole order such as E3, M4, E4, etc., and deliver mixing ratios δ of mixed magnetic and electric nature.Show more - ItemAnomalous scaling of dynamical large deviations(American Physical Society, 2018) Nickelsen, Daniel; Touchette, Hugo
Show more The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium systems. The definition of these functions involves a scaling limit, similar to the thermodynamic limit, in which the integration time τ appears linearly, unless the process considered has long-range correlations, in which case τ is generally replaced by τξ with ξ≠1. Here, we show that such an anomalous power-law scaling in time of large deviations can also arise without long-range correlations in Markovian processes as simple as the Langevin equation. We describe the mechanism underlying this scaling using path integrals and discuss its physical consequences for more general processes.Show more - ItemApplication of the relativistic random-phase and distorted wave impulse approximations to quasielastic proton-nucleus scattering(Stellenbosch : University of Stellenbosch, 2010-12) Van Niekerk, David Douglas; Van der Ventel, B. I. S.; Hillhouse, G. C.; University of Stellenbosch. Faculty of Science. Dept. of Physics.
Show more ENGLISH ABSTRACT: In this dissertation a fully relativistic model for polarized inclusive quasielastic proton-nucleus scattering is developed. Using a standard relativistic impulse approximation (RIA) treatment of quasielastic scattering and a two-body SPVAT form of the current operator, it is shown how the behaviour of projectile and target can be decoupled. Subsequently, different models for projectile and target can be adopted and combined to examine a variety of relativistic effects. The most simplistic model of the target is provided by a mean-field nuclear matter approximation to the relativistic meson-nucleon model, quantum hadrodynamics (QHD). Here relativistic effects manifest as an effective mass, which is lower than the free mass, of the constituent nucleons. This model is improved upon by including many-body correlations through medium-modification of meson propagators in the relativistic random-phase approximation (RPA). Since it is generally accepted that the strong nuclear force and the extended range of the nuclear potential lead to distortion effects on the projectile and ejectile (seen as a modulation of the wave functions), our formalism is geared towards the use of relativistic distorted waves (RDWIA). The distorted waves are written as partial wave expansions and are solutions to the Dirac equation with potentials. The inclusion of distortions, however, greatly increases the computational burden and we show how a number of analytical and numerical techniques can be used to facilitate the process of calculation. It is also shown how the standard relativistic plane wave treatment (RPWIA) can, instead, be easily employed to obtain a baseline for determining the impact of distortions. A calculation is performed for the reaction 40Ca(!p, !p !) at a beam energy of 500 MeV. Here it is found that the effect of correlations on the RPWIA calculation can be seen as a quenching of the cross section that is expected to become more pronounced at lower energies or for higher density targets. A RDWIA calculation shows additional reduction and if target correlations are included this effect is enhanced. To our knowledge this is the first calculation that attempts to include both these effects (RPA and RDWIA) in the context of quasielastic proton-nucleus scattering.Show more - ItemAspects of femtosecond pulse shape transfer via difference frequency mixing(Stellenbosch : Stellenbosch University, 2015-12) Botha, Gerda Nicolene; Uys, Hermann; Schwoerer, Heinrich; Stellenbosch University. Faculty of Science. Dept. of Physics.
Show more ENGLISH ABSTRACT: We investigate the generation of shaped femtosecond pulses in the infrared spectral regime via a nonlinear process called di erence frequency mixing. First we develop a detailed model of the process, incorporating pulse propagation during di erence frequency mixing, in the slowly varying envelope approximation. Di erence frequency mixing (DFM) is numerically simulated for several wavelengths, nonlinear crystals and Type I and Type II frequency mixing. The di erent factors in uencing the shape transfer e ciency of a shaped pulse to a di erent wavelength regime, as well as the conversion e ciency, is identi ed and investigated thoroughly by doing a parametric study. The numerical modeling demonstrates that the e ciency, with which a shaped pulse in the near-infrared is transferred to another wavelength regime, depends strongly on the refractive index of the nonlinear medium for the interacting pulses and is optimal when the velocity of the generated pulse equals that of the shaped input pulse. We show that it is possible to control the temporal pulse duration of the generated pulse by using speci c input angles and so manipulating the e ective refractive index of the nonlinear material for the input and generated pulses. It was found that it is possible to temporally broaden or narrow the generated pulse relative to the input pulses. We compare the developed numerical model to experimental measurements. A liquid crystal spatial light modulator (SLM), inserted in a 4f setup, is used to generate the shaped pulses. Experimentally we demonstrate high- delity shape transfer by mixing 795 nm and 398 nm femtosecond pulses in a BBO crystal. The temporal broadening and narrowing of the generated pulse is also shown and compared to the numerical simulations showing excellent agreement with measured results.Show more - ItemAspects of quantum field theories(Stellenbosch : Stellenbosch University, 1997) Van Biljon, Andrew; Scholtz, Frederik G.; Stellenbosch University. Faculty of Science. Department of Physics.
Show more ENGLISH ABSTRACT: In this study project we give a general introduction to quantum field theories. In the first chapter we revise the operator formalism of quantum mechanics as well as the second quantization scheme that is used to describe many-particle systems. In the second chapter we develop the idea of path integrals within a quantum mechanics framework. We then apply path integral formalism developed in chapter two to introduce quantum field theories. We describe a field theory for scalar fields in chapter three and then a field theory for fermion fields in chapter four as well as the renormalization techniques in chapter five. In chapter six we show how scattering amplitudes are related to Green's functions which are derived from the path integral formalism. In the last chapter we give a brief introduction to gauge field theories.Show more - ItemAtmospheric heavy metal deposition in North Macedonia from 2002 to 2010 studied by Moss biomonitoring technique(MDPI, 2020-08-30) Barandovski, Lambe; Stafilov, Trajce; Sajn, Robert; Frontasyeva, Marina; Andonovska, Katerina Baceva
Show more Moss biomonitoring technique was used for a heavy-metal pollution study in Macedonia in the framework of the International Cooperative Program on Effects of Air Pollution on Natural Vegetation and Crops (UNECE IPC Vegetation). Moss samples (n = 72) were collected during the summers of 2002, 2005, and 2010. The contents of 41 elements were determined by neutron activation analysis, atomic absorption spectrometry, and inductively coupled plasma atomic emission spectrometry. Using factor and cluster analyses, three geogenic factors were determined (Factor 1, including Al, As, Co, Cs, Fe, Hf, Na, Rb, Sc, Ta, Th, Ti, U, V, Zr, and rare-earth elements–RE; Factor 4 with Ba, K, and Sr; and Factor 5 with Br and I), one anthropogenic factor (Factor 2, including Cd, Pb, Sb, and Zn), and one geogenic-anthropogenic factor (Factor 3, including Cr and Ni). The highest anthropogenic impact of heavy metal to the air pollution in the country was from the ferronickel smelter near Kavadraci (Ni and Cr), the lead and zinc mines in the vicinity of Makedonska Kamenica, Probištip, and Kriva Palanka in the eastern part of the country (Cd, Pb, and Zn), and the former lead and zinc smelter plant in Veles. Beside the anthropogenic influences, the lithology and the composition of the soil also play an important role in the distribution of the elements.Show more - ItemAttractive electromagnetic Casimir stress on a spherical dielectric shell(Elsevier, 2013) Graham, N.; Quandt, M.; Weigel, H.
Show more Based on calculations involving an idealized boundary condition, it has long been assumed that the stress on a spherical conducting shell is repulsive. We use the more realistic case of a Drude dielectric to show that the stress is attractive, matching the generic behavior of Casimir forces in electromagnetism. We trace the discrepancy between these two cases to interactions between the electromagnetic quantum fluctuations and the dielectric material.Show more - ItemBasic concepts of random matrix theory(Stellenbosch : University of Stellenbosch, 2005-12) Van Zyl, Alexis J.; Scholtz, Frederik G.; University of Stellenbosch. Faculty of Science. Dept. of Physics.
Show more It was Wigner that in the 1950’s first introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of Random Matrix Theory has grown tremendously, with applications ranging from fluctuations on the economic markets to M-theory. It is the purpose of this thesis to discuss the basic concepts of Random Matrix Theory, using the ensembles of random matrices originally introduced by Wigner, the Gaussian ensembles, as a starting point. As Random Matrix Theory is classically concerned with the statistical properties of levels sequences, we start with a brief introduction to the statistical analysis of a level sequence before getting to the introduction of the Gaussian ensembles. With the ensembles defined, we move on to the statistical properties that they predict. In the light of these predictions, a few of the classical applications of Random Matrix Theory are discussed, and as an example of some of the important concepts, the Anderson model of localization is investigated in some detail.Show more - ItemBayesian parameter estimation for discrete data spectra(Stellenbosch : Stellenbosch University, 2017-12) Wang, Li; Eggers, H. C.; Stellenbosch University. Faculty of Science. Dept. of Physics.
Show more ENGLISH ABSTRACT : Discrete spectra are ubiquitous in physics; for example nuclear physics, laser physics and experimental high energy physics measure integer counts in the form of particles in dependence of angle, wavelength, energy etc. Bayesian parameter estimation ( tting a function with free parameters to the data) is a sophisticated framework which can handle cases of sparse data as well as input of pertinent background information into the data analysis in the form of a prior probability. Bayesian comparison of competing models and functions takes into account all possible parameter values rather than just the best t values. We rst review the general statistical basis of data analysis, focusing in particular on the Poisson, Negative Binomial and associated distributions. After introducing the conceptual shift and basic relations of the Bayesian approach, we show how these distributions can be combined with arbitrary model functions and data counts to yield two general discrete likelihoods. While we keep an eye on the asymptotic behaviour as useful analytical checks, we then introduce and review the theoretical basis for Markov Chain Monte Carlo numerical methods and show how these are applied in practice in the Metropolis-Hastings and Nested Sampling algorithms. We proceed to apply these to a number of simple situations based on simulation of a background plus two or three Gaussian peaks with both Poisson and Negative Binomial likelihoods, and discuss how to select models based on numerical outputs.Show more - ItemBiofilament interacting with molecular motors(Stellenbosch : Stellenbosch University, 2015-12) Meylahn, Janusz Martin; Muller-Nedebock, Kristian K.; Touchette, Hugo; Stellenbosch University. Faculty of Science. Dept. of Physics.
Show more ENGLISH ABSTRACT: We study molecular motors moving along a filament or polymer using two different mathematical models in which motors are idealised as springs. In the first model we study the average and the fluctuations of the motor stretch by modelling the motion of the motors along the filament using a simple stochastic differential equation with linear friction. We use the notion of stochastic resetting to explicitly include the attachment and detachment dynamics of the motors to and from the filament and study the fluctuations around the most probable value of the mean stretch using methods from large deviation theory. The second model uses methods from field theory to model a dynamic network consisting of a single polymer and many molecular motors. In this case, we develop techniques to include the bias motion of the molecular motors in a weighting factor for the formation of specific networks rather than in the dynamical constraints of the partition function which allows us to study the steady-state of the network using a self-consistency argument and a saddlepoint approximation.Show more