Имитационное моделирование процесса деструкции полимера

This thesis is centered on the theory of stochastic processes and their applications in biological systems characterized by a complex environment. Three case studies have been modeled by the use of the three fundamental tools of stochastic processes: the master equation (ME), the stochastic differential equation (SDE) and the partial differential equation (PDE). The principal approach here applied to deal with complexity is the characterization of the system by means of probability distributions describing each a parameter of the model or the introduction of fractional order derivatives to include non-local and memory effects maintaining the linearity in the equations. In Chapter 1 we briefly review the theory of stochastic processes. In Chapter 2 we derive a birth-death process master equation to test if Long Interspersed Elements (LINEs) can be modeled according to the neutral theory of biodiversity. In Chapter 3 we derive a model of anomalous diffusion based on a Langevin approach in which anomalous behavior arise in the asymptotic intermediate state as a consequence of the heterogeneity of the system, from the superposition of Ornstein-Uhlenback processes. In Chapter 4 we propose an extension of the cable equation, used to describe anomalous diffusion phenomena as the signal conduction in spiny dendrites, by introducing a Caputo time fractional derivative.

Although current water desalination technologies are mature enough and advanced, the shortage of freshwater is still considered as one of the most pressing global issues. Therefore, there is a strong incentive to explore and investigate new potential methods with low energy consumption. It is well-known that polymer hydrogel network has the ability to absorb water via swelling. In the case of polyelectrolyte hydrogels, the charges localized on the polymer chains, which mainly drive the swelling pressure inside the hydrogel, can also separate added salt via charge-based selectivity (Donnan exclusion). When combining this material with a temperature-sensitive polymer, the heat generated by solar energy can trigger the desorption process via conformational change of polymer chains. Hence, hydrogels designed from both materials, polyelectrolyte and thermo-responsive polymer can reduce the salinity of water, such as brackish water by means of reversible thermally-induced absorption and desorption desalination processes. In addition, the desorption process can also be achieved based solely on a polyelectrolyte hydrogel system by altering the ionization of charges within the hydrogel via pH. In this thesis, hydrogel-based water desalination process were developed using acrylic acid (AAc)/sodium acrylate (SA)-based polyelectrolytes as the charge-based separation function, alone or with a combination of N-isopropylacrylamide (NIPAAm) as thermo-responsive comonomer. In the latter case, a series of chemically cross-linked polymeric hydrogels were synthesized via either free radical-initiated copolymerization or reversible addition-fragmentation chain transfer (RAFT) polymerization, thus realizing different macromolecular architecture. According to the nature of hydrogels, the reversible sorption/desorption state were triggered by either chemical stimulus (pH), or physical stimulus (heat) as the thermo-responsive polymer introduced into the hydrogels. In detail, the effect of hydrogel composition as well as the influence of the macromolecular architecture on the swelling/deswelling behavior for the synthesized hydrogels were studied. For this, their properties including their responses to external stimuli were investigated, and their ability to desalinate brackish water as well as the effciency of such desalination process were evaluated. Generally, the results demonstrated correlations between macromolecular architecture of the network structure and their performance in the proposed desalination process, such as salt rejection and desalination capacity. Moreover, the potential of the best performance materials for applications was also discussed.

Whether or not a time series is weakly stationary has long been a question of major interest in the field of time series analysis. Stationary time series can be sufficiently described by means of autoregressive moving average (ARMA) processes. When modelling temporal correlations of GNSS observation noise, the applicability of ARMA processes depends on the stationarity of residual time series from GNSS data analysis. According to the property that stationary processes have homogenous variances, statistical inferences on stationarity can be made by testing for homogeneity of variance (HOV). In addition, considering a time series as a realisation of a stochastic process, stationarity can be assessed by testing for stochastic trends using unit root tests. Based on representative data simulations, this paper analyses the empirical size and power of commonly used HOV and unit root tests. The results show that the performance of the HOV test is strongly affected by serial correlations, whereas the unit root test produces high power without significant size distortions.

In this thesis we used single-molecule FRET to investigate the kinetic properties of a protein called Argonaute. While traditionally one uses bulk methods to investigate the molecular properties of proteins, bulk methods do not confer information that is transient, since that is inherently averaged out. Single-molecule methods, as their name imply, allow one to observe interactions between individual molecules and their substrates. This allows one to see fast kinetics which may otherwise be missed. Furthermore, while the bulk methods give one only the average kinetics, single molecule methods also give the distribution of probabilities to access certain bound or conformational states, which in turn can give the observer information of the nature of the stochastic process. We rely in this thesis on single-molecule FRET, an abbreviation for Forster Resonance Energy Transfer: It’s a process where energy is transferred through dipole-dipole interaction from a donor fluorophore to an acceptor fluorophore. The distance between fluorophores determines the efficiency of transfer on a length scale of » 10 nm. Since many biological processes take place on this length scale, this technique is exquisitely suitable to study biological processes real-time on the smallest scale, whether it is conformational changes, protein-protein interactions, or in this case, protein target search studies.

In this thesis, stochastic processes closely related to a prominent process called Brownian motion is introduced. The processes are called local Brownian motions. Two rich families are constructed, which can be used to model stochastic dynamical systems in such fields as finance, biology, and physics. Stochastic calculus with respect to local Brownian motion is developed, and strong solutions are presented for some stochastic differential equations driven by the noise generated by local Brownian motions.

Bacteria are exposed to fluctuations in their environment and can respond to such changes by regulating gene expression, often at the level of transcription. Since gene expression is an inherently stochastic process, identical cells within a single environment display heterogeneous expression levels. To understand how the stochastic processes in gene expression affect the dynamics of single-cell gene regulation it is necessary to observe gene expression in single cells in changing environments. Recently developed microfluidic devices combined with quantitative fluorescence time-lapse microscopy allow lineages of single cells to be followed over long timescales and to measure their growth and gene expression phenotypes simultaneously. However these devices are missing the environmental control needed to study gene regulation. Therefore we set out to find a way to combine the longterm observation of single cells with precise environmental control in a single microfluidic chip. As a basis we chose a device called the Mother Machine in which single files of cells are growing in small dead end growth channels. These growth channels are connected to a main channel with a constant flow of medium for nutrient diffusion into the growth channels. The cells at the dead end of the growth channels are trapped and when dividing push their progeny into the main channel where they are removed by the flow. Therefore the trapped cell can be monitored essentially for its whole lifetime, while its progeny can only be observed for a short timeframe before they leave the growth channel. By combining the Mother Machine design with a specialized dual input junction and mixing serpentines for environmental control we developed a device that offers new prospects in studying gene regulation. Together with the device we developed an easy to use software solution to analyze data from Mother Machine like devices together with our collaboration partners. This integrated experimental and computational setup will be an important tool to understand the genetic basis for differences in single-cell expression distributions, and to understand how natural selection has shaped single-cell gene regulation. As a first example we show how single cells differ in the regulation of the expression of the lac operon when exposed to alternating changes in the available carbon source switching between glucose and lactose every 4h.

Interfacial delamination in polymer coated metal sheet : a numerical-experimental study

The Next Generation Sequencing (NGS) revolutionized the quality and quantity of the genetic data delivered. To extract all the benefits of the new technique there is an urge of precise inference rules built from a strong theoretical basis. In the presentation I will provide a novel, extended way of looking at NGS data. The NGS experiment can<br>be interpreted as a process of mapping short fragments of sequences (short reads) to a genome region of interest (exon , gene, gene family or even whole chromosome) and the activity of a region, is derived from the number of successful mappings. The increased reliability and the design of the NGS experiments allows for a more sophisticated<br>mathematical framework which uses not only the intensity of expression but also the position of particular reads aligned to the genomic region. To account for both aspects, in my presentation I introduce the Poisson point process framework for the NGS experiments. In this approach the reference genome coordinate information of the mapped reads implies that the differences in activity can arise also in changes of read positioning. Using the<br>inference tools for stochastic point processes combined with functional data analysis I provide a method to quantify the activity differences in terms of both - the intensity and positioning - through the phase-amplitude separation. As a consequence I revisit the problem of the variability in NGS data and indicate, how it can be understood through the phase-amplitude dichotomy. Finally I will show that the new approach can reveal additional<br>information in the genetic data. The proposed method can be effectively utilized in detecting events of alternative splicing, exon blocking, exon skipping, can be also thought of as a new setting for inference on NGS data.

Stochastic wave models play a central role in our present-day wave modelling capabilities. They are frequently used to compute wave statistics, to generate boundary conditions and to include wave effects in coupled model systems. Historically, such models were developed to predict the wave field evolution in deep water where the conditions of Gaussianity generally hold. However, in recent decades, such models have been applied to the shallower coastal environment where the stochastic representation of the dominant wave physics becomes questionable. This is primarily due to the increased influence of wave nonlinearity and the additional depth-induced wave processes that are dominant in this region.&lt;br/&gt;&lt;br/&gt;Unfortunately, the two most dominant wave processes in the surf zone: depth-induced wave breaking and nonlinear triad wave-wave interactions are also the least well represented and understood. This is due to both their complexity and the scarcity of analytical solutions for realistic wave fields. As such, they represent a significant obstacle in the accurate modelling of the wave dynamics in the coastal region. Providing accurate representations of these wave processes is essential to answering the questions demanded from stochastic wave models from coastal engineers for coastal management and design. Such advancements are necessary to improve our understanding of wave-induced processes, to reduce costs in managing the coastal environment and to tackle contemporary issues such as uncertainties with respect to increased sea level rise.&lt;br/&gt;&lt;br/&gt;Due to the complexity of depth-induced wave breaking, a complete representation of this wave process does not exist for both stochastic and deterministic modelling frameworks. Although there is extensive literature on the subject of parameterizing depth-induced wave breaking in a stochastic sense, these parameterizations are inconsistent with theory, observations and (deterministic) model predictions. In particular, present-day modelling defaults perform poorly over (near-)horizontal bathymetries with over-enhanced wave dissipation of locally-generated waves and insufficient dissipation of swell waves. Equally, nonlinear triad wave-wave interactions are poorly represented in stochastic wave models due to the problem of closure and the impractical computational expense of more accurate representations. In particular, the most commonly applied parameterization in the wave literature incorrectly predicts the evolution of the spectral shape, and the convergence to an equilibrium high-frequency tail deep in the surf zone. Correctly resolving these issues is essential for the management of many of the activities occurring at the coast; from the design of coastal defenses to feasibility studies for wave energy converters, from port operation and availability to vessel navigation, from understanding the ecology at the coast to the fisheries, and from managing leisure and tourism to safety at the coast.&lt;br/&gt;&lt;br/&gt; In this work, we investigate the process of depth-induced wave breaking through a comprehensive analysis of the literature and a comparison of modelling performance. Here, we use an extensive set of wave observations representing a large range of wave conditions and bathymetric profiles. The analysis demonstrates that no currently available depth-induced breaking source term is capable of sufficiently representing the process of depth-induced wave breaking. This is shown to be in agreement with the wave literature with parameterizations either over-predicting wave dissipation for locally generated waves or under-predicting wave dissipation for non-locally generated waves over (near-)horizontal bathymetries. To address this issue, a new joint scaling using both local wave and bathymetric conditions is proposed. Using both the normalized characteristic wave number and local bottom slope unifies two approaches prevalent in the wave literature. This is shown to improve the model performance for the dissipation of both locally and non-locally generated waves over (near-)horizontal bathymetries. &lt;br/&gt;&lt;br/&gt;Furthermore, the validity of the assumption that wave dissipation can be modelled as analogous to a 1D dissipative bore is explored. Subsequently, a heuristic directional modification is introduced for depth-induced wave breaking dissipation models. This directionally partitions the 2D spectrum into several directional partitions that are assumed to be unidirectional. Model results demonstrate that the effect of the directional partitioning is to reduce the dissipation of wave energy and to enhance the significant wave height; in agreement with field measurements. Not only is this modification shown to be applicable to the joint wave breaking parameterization proposed in this study, but also for well-established parameterizations. &lt;br/&gt;&lt;br/&gt;The effects of both the proposed scaling and directional modification are then reviewed from an operational context and are compared to state-of-the-art source terms, field observations and a hypothetical storm representative of Dutch design conditions. Such design conditions are expected to be representative of design conditions found globally. In an environment where storm intensities may be increasing, for example due to global warming, the results of wave breaking models near the coast under such extreme conditions become of greater relevance. The influence of wave breaking models in coupled model systems is anticipated to provide important new insights in understanding the various wave-driven processes along our coasts. &lt;br/&gt;&lt;br/&gt;Next, the representation of the nonlinear triad wave-wave interactions in stochastic wave models is reviewed. In particular, the collinear approximation used to transform 1D triad source terms for implementation in 2D stochastic wave models is revisited. These approximations are necessitated by considerations of computational efficiency. The conventional collinear approximation is shown to be inconsistent at the unidirectional limit and to be a primary source of modelling error. Instead of converging to the values predicted by the 1D triad source terms at the unidirectional limit, the energy transfers as computed by stochastic wave models are shown to become unbounded. This results in a dimensional calibration coefficient which is at least an order of magnitude smaller than that found in the wave literature. Consequently, for directional wave conditions, 1D triad source terms implemented with the conventional collinear approximation insufficiently capture the wave evolution. To address this problem, a new collinear approximation is presented which accounts for the wave energy contained within a finite directional bandwidth. This collinear approximation is shown to converge correctly at the unidirectional limit and to agree well with predictions from a second-order accurate deterministic wave model. In particular, better agreement is shown in the modelling prediction of the spectral shape and related integral parameters, e.g. wave period, under idealized wave conditions. Under certain conditions, these error reductions are shown to be more significant than differences between the underlying triad models.&lt;br/&gt;&lt;br/&gt;The contribution of this work demonstrates that while the underlying theory underpinning stochastic wave modelling in the coastal environment still remains questionable, the accurate determination of wave statistics in the coastal zone is tenable. With the advancements presented in this study, the new source terms correspond better with the current wave literature and are shown to provide significant steps forward over existing default source terms. The developments presented here are anticipated to form the foundation for future source term research, and to be used for the representation of the dominant wave physics in the coastal environment in operational wave models.

Polymer photovoltaic cells currently achieve power conversion efficiencies (PCE) above 10% on lab scale. To compete with the efficiencies above 20% of inorganic solar cells, understanding and elimination of all the loss channels is necessary. This thesis investigates charge generation and recombination processes in polymer-fullerene solar cells with the aim of elucidating the nature of such losses. Chapter 1 provides a general introduction to the subject of the thesis and an overview of the most relevant literature. In Chapter 2 the effect of the thermodynamic driving force on the efficiency of photoinduced charge transfer between semiconducting polymers and fullerene is investigated. A polyfluorene copolymer is mixed with a variety of fullerene mono- and bisadducts having different LUMO energy levels. The difference in LUMO energy of the acceptors results in different energies of the charge transfer (CT) states in the blends. By spectroscopic characterization of bulk heterojunction thin films and photovoltaic devices it is found that the CT state needs to be at least 0.1 eV lower in energy than the singlet excited state of the fullerene to be formed efficiently. The central finding of Chapters 3 to 5 is that the nanoscale morphology of the polymer-fullerene heterojunction strongly influences the CT state dissociation and recombination. Blends composed of a small optical bandgap semiconducting polymer (PCPDTBT) mixed with fullerene are studied with various techniques. The nanoscale phase separation of these blends is controlled by adding high-boiling point co-solvents to the solutions used to process the thin films. Without co-solvent the blends are very finely mixed and the addition of co-solvents increases the phase separation. In blends that are too finely mixed we observe recombination of the CT state to the triplet state of the polymer (Chapter 3). We monitor the formation of triplets and charges in the thin films by means of photo-induced absorption (PIA).The recombination to the triplet state is a loss mechanism, in competition with the dissociation of the CT state into free charges. This process is reduced in favor of free charge formation when the phase separation is increased, correlating with the increased device performance. Specifically, increased fill factor and short circuit current are observed in the devices with optimized morphology. These results show that photophysical processes are controlled by the nanoscale morphology. In Chapter 4 we perform charge extraction experiments on solar cells having different nanoscale phase separation and we support the results with PIA experiments on corresponding thin films. In the charge extraction and PIA experiments we study the same set of long lived charges. We confirm that CT recombination (to the triplet and to the ground state) is largely responsible for the poor device performances of not-optimized blends. Finally, in Chapter 5 we show a correlation between population of triplet excited states and decreased photo-stability of the blends. We suggest that triplet states can lead to the formation of singlet oxygen, which in turn can initiate destructive chemical reactions in the polymer chains. In Chapters 6 and 7 the influence of excess photon energy (i.e. the difference between the energy of the absorbed photon and that of the CT state) in the CT state dissociation is investigated by means of charge extraction and spectral response measurements in different polymer:fullerene blends. We find that excess energy is not necessary for CT dissociation in blends with coarse phase separation. A measurable influence of the excess photon energy on CT dissociation is observed only in PCPDTBT:PCBM finely dispersed blends, which were shown in the previous chapters to be strongly affected by CT state recombination. Chapter 8 investigates what is limiting the photo-current of solar cells close to the open-circuit voltage. It is found that under these conditions space-charge can build up, so that the photocurrent becomes space-charge limited. This condition is reached only in blends where CT dissociation is efficient at low electric fields. Impedance spectroscopy is the technique used here. The experimental results are supported by an analytical model and by drift diffusion simulations. Summarizing, in this thesis it is shown that the CT state is a critical intermediate state in the charge generation process in polymer solar cells. The energy of the CT state needs to be low enough to convert neutral excitations into charges. The blend morphology is a crucial factor determining the branching ratio between dissociation into free carriers and recombination to the ground state or to the triplet state of the polymer.

Conventional amphiphilic block copolymers are macromolecules consisting of at least a hydrophilic segment covalently attached to a hydrophobic segment. They are unique and versatile building blocks in supramolecular polymer chemistry, both for the generation of highly organized, self-assembled structures and for the structural control of material interfaces. In the absence of solvents, the phase-behavior of block-copolymers is sparingly described. In aqueous solutions block copolymers self-assemble into nanoscopic objects. These structures are gaining more and more attention for technical formulations. Self-assembly is simply induced by dissolving dry powder of amphiphilic copolymers in water. This self-assembly process, however, cannot be described solely based on bulk phase behavior and very few experimental phase diagrams of block copolymer/water mixtures have been reported. In order to control, predict and eventually achieve a comprehensive understanding of this process and in particular the formation of vesicles, worm/rod-like micelles and spherical micelles it is important to systematically investigate the phase behavior of block copolymers across the whole water concentration range. We therefore undertook investigations of the self-assembly of two block copolymers. Preliminary encapsulation studies reveal their potential for applications relevant for drug delivery. &#13;\nThe concentration profile of the identified amphiphilic block-copolymers diluted in aqueous solution was examined across the whole concentration range with four poly(ethylene oxide)-block-poly(γ-methyl-ε-caprolactone) (PEO-b-PMCL) block copolymers keeping the hydrophilic block length constant but varying the hydrophobic lengths. Bulk polymers did not display any ordered morphology. With increasing water concentrations the polymers underwent transitions from lamellar phases to packed vesicles and eventually all polymers self-assembled into vesicles in dilute aqueous solutions. At high concentration the largest polymer organized further into an inverse hexagonal phase prior to self-assembly into a lamellar phase. The smallest block-copolymer also self-aggregated into rod-like micelles and exhibited a hexagonal phase between the packing of the rod-like micelles/vesicles and the lamellar phase.&#13;\nThe concentration profile of phases assembled by amphiphilic block-copolymers diluted in aqueous solution was examined as well across the whole concentration range with three poly(isobutylene)-block-poly(ethylene oxide) block copolymers having the same hydrophobic block length but varying in their hydrophilic lengths. In contrast to PEO-b-PMCL these polymers self-aggregated depending on the hydrophilic length into micelles, worm-like micelles and for the shortest polymer into vesicles. Thus, increasing the polymer concentration lead to a different phase behavior. The largest polymer which solely formed micelles, underwent transitions from packed micelles with a few packed worm-like micelles to a hexagonal phase and finally into a lamellar phase, in contrary to the middle length polymer, which self-aggregated into worm-like micelles. The best to our knowledge, it is the first time that an experimental phase diagram is built such that it displays the formation of worm/rod-like micelles. With the composition studied in here, the worms, with increasing polymer concentration, pack and undergo afterwards into a hexagonal and finally a lamellar phase has been observed. For the shortest polymer the phase behavior was similar to that of vesicles self-assembled by PEO-b-PMCL. In contrast, the pure polymer formed an inverse hexagonal phase.&#13;\nIt was eventually shown that PEO23-PMCl32 can be used to encapsulate both small and large molecules. By adjusting the pH towards acidic conditions the responsiveness of the vesicles could be triggered to release the encapsulated material.

In the following Part II the deterministic and stochastic laws of motion arising from the processes depicted in Part I (particulary Section 2), are analyzed in detail. In section 4 we study the typical non-linear logistic model emerging as the deterministic equivalent of the diffusion processes of Sections 2.3 and 2.4. The interaction of firm size and firm number are also studied within the same Section. In Section 5 we analyze the (asymptotic) stochastic laws of motion of the system. In particular, we study the Langevin equation and the approximations of the Fokker-Planck equations equivalent of the master equations of the same stochastic processes. We see that stochastic laws of motion may not be equivalent (not even asymptotically) to deterministic ones (e.g. Due to variance effects which determine increasingly larger fluctuations).

Extreme conditions involve low or high temperatures (> 1500 K), high pressures (> 30 MPa), high strains or strain rates, high radiation fluxes (> 100 dpa), and high electromagnetic fields (> 15T). Material properties under extreme conditions can be extremely different from those under normal conditions. Understanding material properties and performance under extreme conditions, including their dynamic evolution over time, plays an essential role in improving material properties and developing novel materials with desired properties. To understand material properties under extreme conditions, we use molecular dynamics (MD) simulations with recently developed reactive force fields (ReaxFF) and traditional embedded atom methods (EAM) potentials to examine various materials (e.g., energetic materials and binary liquids) and processes. The key results from the simulations are summarized below. Anisotropic sensitivity of RDX crystals: Based on the compress-and-shear reactive dynamics (CS-RD) simulations of cyclotrimethylene trinitramine (RDX) crystals, we predict that for mechanical shocks between 3 and 7 GPa, RDX is the most sensitive to shocks perpendicular to the (100) and (210) planes, while it is insensitive to those perpendicular to the (120), (111), and (110) planes. The simulations demonstrate that the molecular origin of anisotropic shock sensitivity is the steric hindrance to shearing of adjacent slip planes. Mechanisms of hotspot formation in polymer bonded explosives (PBXs): The simulations of a realistic model of PBXs reveal that hotspots may form at the nonplanar interfaces where shear relaxation leads to a dramatic temperature increase that persists long after the shock front has passed the interface. For energetic materials this temperature increase is coupled to chemical reactions that eventually lead to detonation. We show that decreasing the density of the binder eliminates the hotspots or reduces the sensitivity. Cavitation in binary metallic liquids: We demonstrate the stochastic nature of the cavitation process in binary metallic liquids, and that classical nucleation theory can predict the cavitation rate if we incorporate the Tolman length derived from the MD simulations. Synthesis the single metallic glass on amorphous substrate: We show that single component metallic glasses (SCMGs) can be synthesized by thermal spray coating of nanodroplets onto an amorphous substrate (ND-AS). The key requirements to form the SCMGs are the rapid cooling rates and the amorphous substrates. Carbon and hydrogen phases under extreme conditions: we report on the use of electron force fields (eFF) in characterizing the Hugoniot relationships of carbon, which includes consecutive phase transitions also captured by experiments, as well as the Hugonoit states of hydrogen centered at various initial densities compared to experiments and the predictions of other theories.

Reaction-diffusion processes in biological systems have been studied using a range of mathematical- and simulation-based approaches. In this thesis, novel techniques and algorithms are developed for reaction-diffusion processes based on Smoluchowski kinetics to simulate reversible reactions of any order. Simulating such reactions sheds light on the dynamics of Wnt signalling, an important biological process which regulates embryonic development, tissue homoeostasis, and diseases such as cancer. A detailed analysis into the fundamental dynamical properties of Wnt signalling helps explore the relationship between signalling mechanisms, protein binding affinities and the end product of cell fate.

Linear viscoelastic behaviors for diglycidyl ether of bisphenol-A epoxy (DGEBA) resins cured with 4,4’-methylenedianaline (MDA) have been studied. For a particular DGEBA/MDA material with a glass transition temperature (Tg) of 102 °C, dynamic shear moduli were measured from 10-2 to 101.7 Hz for 41 temperatures between −150 °C and 180 °C. Because DGEBA/MDA epoxies are thermorheologically complex, construction of master curves via time-temperature superposition is not applicable. Stress relaxation experiments were performed from 90 °C to 112.5 °C using the same specimen. A combination of Fourier transformed transient data and dynamic data extended the frequency window of an isotherm to 6 orders of magnitude. A new methodology was developed for determining the relaxation spectrum, where the spectral density changes under the constraint that all spectral components have the same strength. This new method accommodates thermorheological complexity. The analysis was performed throughout the entire temperature range, including sub-Tg low-temperature glassy state (i.e., γ region), sub-Tg “excess wing” (i.e., β region), glass-to-rubber transition zone (i.e., α region), and above-Tg plateau and terminal zones. In sub-Tg γ and β regions, dielectric relaxation data were analyzed using the same method. Spectral analysis was applied to a variety of glassy-forming materials, including linear polymers, crosslinked polymers, oligomers and small molecules, with a focus on the relaxation processes in glass-to-rubber transition region (i.e., near and above α region). Spectra were constructed from (i) experimental data of a series of linear and crosslinked DGEBA polymers with different crosslink densities, and (ii) digitized literature data consisting storage and loss isotherms near and above Tg. A second relaxation process was found at higher temperatures and longer relaxation times than the main α peak, which is designated as the “α+” process, where the molecular mechanism of α+ is unknown. For molecular glass formers no α+ process is observed. For other materials the α+ process is present as a shoulder on α peak. In addition to temperature, deformation also affects mobility, where in the absence of deformation the mobility will decrease as the materials evolves towards the equilibrium state in a process called “physical aging”. Two major ideas how mobility is affected by deformation: rejuvenation and accelerated aging. In accelerated aging, the molecular mobility is decreased after deformation. In rejuvenation, the mobility will increase. To discriminate these two models, a set of 4-step non-linear tensile experiments were performed on a crosslinked DGEBA polymer at Tg – 16 °C. The effect of deformation history was evaluated by comparing the mobility before and after the large deformation, where the mobility was quantified as the magnitude of stress overshoot on a stress-strain curve during reloading in the 4-step experiment. The experimental results at Tg – 16 °C are predominantly due to aging effect but the aging is not accelerated by the presence of deformation history.