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In order to permeate a nanopore, an ion must overcome a dehydration energy barrier caused by the redistribution of surrounding water molecules. The redistribution is inhomogeneous, anisotropic and strongly position-dependent, resulting in complex patterns that are routinely observed in molecular dynamics simulations. Here, we study the physical origin of these patterns and of how they can be predicted and controlled. We introduce an analytic model able to predict the patterns in a graphene nanopore in terms of experimentally accessible radial distribution functions, giving results that agree well with molecular dynamics simulations. The patterns are attributable to a complex interplay of ionic hydration shells with water layers adjacent to the graphene membrane and with the hydration cloud of the nanopore rim atoms, and we discuss ways of controlling them. Our findings pave the way to designing required transport properties into nanoionic devices by optimising the structure of the hydration patterns.

The permeation of ions through narrow water-filled channels is essential to life and of rapidly-growing importance in technology. Reaching an understanding of the mechanisms underlying the permeation process requires an interdisciplinary approach, where ideas drawn from physics are of particular importance and have brought encouraging progress in recent years. This Introduction sets into context the several ground-breaking papers presented in the Entropy Special Issue on “The Physics of Ionic Conduction in Narrow Biological and Artificial Channels.

Biological ion channels are fundamental to maintaining life. In this manuscript we apply our recently developed statistical and linear response theory to investigate Na+ conduction through the prokaryotic Na+ channel NaChBac. This work is extended theoretically by the derivation of ionic conductivity and current in an electrochemical gradient, thus enabling us to compare to a range of whole-cell data sets performed on this channel. Furthermore, we also compare the magnitudes of the currents and populations at each binding site to previously published single-channel recordings and molecular dynamics simulations respectively. In doing so, we find excellent agreement between theory and data, with predicted energy barriers at each of the four binding sites of ∼4,2.9,3.6, and 4kT.

We introduce a statistical and linear response theory of selective conduction in biological ion channels with multiple binding sites and possible point mutations. We derive an effective grand-canonical ensemble and generalised Einstein relations for the selectivity filter, assuming strongly coordinated ionic motion, and allowing for ionic Coulomb blockade. The theory agrees well with data from the KcsA K$^+$ channel and a mutant. We show that the Eisenman relations for thermodynamic selectivity follow from the condition for fast conduction and find that maximum conduction requires the binding sites to be nearly identical.

We consider an atomistic model of thermal welding at the polymer-polymer interface of a polyetherimide/polycarbonate blend, motivated by applications to 3D manufacturing in space. We follow diffusion of semiflexible chains at the interface and analyze strengthening of the samples as a function of the welding time tw by simulating the strain-stress and shear viscosity curves. The time scales for initial wetting, and for fast and slow diffusion, are revealed. It is shown that each component of the polymer blend has its own characteristic time of slow diffusion at the interface. Analysis of strainstress demonstrates saturation of the Young’s modulus at tw = 240 ns, while the tensile strength continues to increase. The shear viscosity is found to have a very weak dependence on the welding time for tw > 60 ns. It is shown that both strain-stress and shear viscosity curves agree with experimental data.

Mutation-induced transformations of conductivity and selectivity in NaChBac bacterial channels are studied experimentally and interpreted within the framework of ionic Coulomb blockade (ICB), while also taking account of resonant quantised dehydration (QD) and site protonation. Site-directed mutagenesis and whole-cell patch-clamp experiments are used to investigate how the fixed charge Qf at the selectivity filter (SF) affects both valence selectivity and same-charge selectivity. The new ICB/QD model predicts that increasing |Qf | should lead to a shift in selectivity sequences towards larger ion sizes, in agreement with the present experiments and with earlier work. Comparison of the model with experimental data leads to the introduction of an effective charge Qf∗ at the SF, which was found to differ between Aspartate and Glutamate charged rings, and also to depend on position within the SF. It is suggested that protonation of the residues within the restricted space of the SF is important in significantly reducing the effective charge of the EEEE ring. Values of Qf∗ derived from experiments on divalent blockade agree well with expectations based on the ICB/QD model and have led to the first demonstration of ICB oscillations in Ca2+ conduction as a function of the fixed charge. Preliminary studies of the dependence of Ca2+ conduction on pH are qualitatively consistent with the predictions of the model.

Selective permeation through graphene nanopores is attracting increasing interest as an efficient and cost-effective technique for water desalination and purification. In this work, using umbrella sampling and molecular dynamics simulations with constant electric field, we analyze the influence of pore charge on potassium and chloride ion permeation. As pore charge is increased, the barrier of the potential of mean force (PMF) gradually decreases until it turns into a well split in two subminima. While in the case of K+ this pattern can be explained as an increasing electrostatic compensation of the desolvation cost, in the case of Cl􀀀 the pattern can be attributed to the accumulation of a concentration polarization layer of potassium ions screening pore charge. Th analysis of potassium PMFs in terms of forces revealed a conflicting influence on permeation of van der Waals and electrostatic forces that both undergo an inversion of their direction as pore charge is increased. Even if the most important transition involves the interplay between the electrostatic forces exerted by graphene and water, the simulations also revealed an important role of the changing distribution of potassium and chloride ions. The influence of pore charge on the orientation of water molecules was also found to affect the van der Waals forces they exert on potassium.

The rising number of small unmanned aerial vehicles (UAVs) expected in the next decade will enable a new series of commercial, service, and military operations in low altitude airspace as well as above densely populated areas. These operations may include on-demand delivery, medical transportation services, law enforcement operations, traffic surveillance and many more. Such unprecedented scenarios create the need for robust, efficient ways to monitor the UAV state in time to guarantee safety and mitigate contingencies throughout the operations. This work proposes a generalized monitoring and prediction methodology that utilizes realtime measurements of an autonomous UAV following a series of way-points. Two different methods, based on sinusoidal acceleration profiles and high-order splines, are utilized to generate the predicted path. The monitoring approach includes dynamic trajectory re-planning in the event of unexpected detour or hovering of the UAV during flight. It can be further extended to different vehicle types, to quantify uncertainty affecting the state variables, e.g., aerodynamic and other environmental effects, and can also be implemented to prognosticate safety-critical metrics which depend on the estimated flight path and required thrust. The proposed framework is implemented on a simplified, scalable UAV modeling and control system traversing 3D trajectories. Results presented include examples of real-time predictions of the UAV trajectories during flight and a critical analysis of the proposed scenarios under uncertainty constraints.

We analyze selective ionic conduction through an artificial nanopore in a single graphene sheet, using molecular dynamics simulations and the prehistory probability distribution. We assess position-dependent changes in the number and orientation of water molecules in the first and second hydration shells of the ion as it crosses the nanopore. We reveal coupling between an ionic double layer near the sheet to the statistical properties of the hydration shells.

We study a molecular dynamics model of a polymer-polymer interface for a polyetherimide/polycarbonate blend, including its thermodynamic properties, its chain reptation, and its corresponding welding characteristics. The strength of the sample is analyzed by measuring strain-stress curves in simulations of uni-axial elongation. The work is motivated by potential applications to 3D manufacturing in space.

Selective permeation through graphene nanopores is attracting increasing interest as an efficient and cost-effective technique for water desalination and purification. In this work, using umbrella sampling and molecular dynamics simulations with constant electric field, we analyze the influence of pore charge on potassium and chloride ion permeation. As pore charge is increased, the barrier of the potential of mean force (PMF) gradually decreases until it turns into a well split in two subminima. While in the case of K

We consider the selective permeation of ions through narrow water-filled channels in the presence of strong interaction between the ions. These interactions lead to highly correlated ionic motion, which can conveniently be described via the concept of a quasiparticle. Here, we connect the quasiparticle’s effective potential and the multi-ion potential of the mean force, found through molecular dynamics simulations, and we validate the method on an analytical toy model of the KcsA channel. Possible future applications of the method to the connection between molecular dynamical calculations and the experimentally measured current-voltage and current-concentration characteristics of the channel are discussed.

We study the highly-concerted motion of ions in anarrow biological ion channel (KcsA) by considering the notionof a quasiparticle, with specific focus on the transition process.Namely, we show that the ion entering or exiting the channelis correlated with the position of the quasiparticle. This resultis of importance in the rate theories of ion conduction throughnarrow channels and artificial nanopores.

The problem of predicting selective transport of ions through nano-pores from their structure in the biological and nano-technological systems is addressed. We use a molecular dynamics simulation to provide insight into the key physical parameters of nano-pores and develop a self-consistent analytic theory describing ionic conduction and selectivity through these devices. We analyse the ion's dehydration and excess chemical potential, derive an expression for the conductivity of the nano-pore, and emphasize the role of fluctuations in its performance. The theory is verified by comparison of the predicted current-voltage characteristics with the molecular dynamics results and experimental data obtained for a graphene nano-pore and the KcsA biological channel.

To establish the general statistical mechanical properties of highly conductive but selective nano-filters we develop an equilibrium statistical-mechanical theory of the KcsA filter, find the probabilities for the filter to bind ions from the mixed intra- and extra-cellular solutions, and evaluate the conductivity of the filter in its linear response regime. The results provide first principles analytical resolution of the long-standing paradox - how can narrow filter conduct potassium ions at nearly the rate of free diffusion while strongly selecting them over sodium ions - and are applicable to a wide range of biological and artificial channels.

We introduce a self-consistent multi-species kinetic theory based on the structure of the narrow voltage-gated potassium channel. Transition rates depend on a complete energy spectrum with contributions including the dehydration amongst species, interaction with the dipolar charge of the filter and, bulk solution properties. It displays high selectivity between species coexisting with fast conductivity, and Coulomb blockade phenomena, and it fits well to data.

Ionic Coulomb blockade (ICB) is an electrostatic phenomenon recently discovered in low-capacitance ion channels/nanopores. Depending on the fixed charge that is present, ICB strongly and selectively influences the ease with which a given type of ion can permeate the pore. The phenomenon arises from the discreteness of the charge-carriers, the dielectric self-energy, an electrostatic exclusion principle, and sequential pore neutralization, and it manifests itself strongly for divalent ions (e.g.\ Ca$^{2+}$). Ionic Coulomb blockade is closely analogous to electronic Coulomb blockade in quantum dots. In addition to the non-local 1D Coulomb interaction considered in the standard Coulomb blockade approach, we now propose a correction to take account of the singular part of the attraction to the binding site (i.e.\ local site binding). We show that this correction leads to a geometry-dependent shift of one of the barrierless resonant conduction points M$_0^{CB}$. We also show that local ion-ion repulsion accounts for a splitting of Ca$^{2+}$ profiles observed earlier in Brownian dynamics simulations., 4 pages, 4 figures, 25 references, ICNF2017 Replacement reasons: Some typo are fixed, notation is optimised)

Background. The selectivity of biological cation channels is defined by a short, narrow selectivity filter, having a negative net fixed charge Qf . Voltage gated bacterial channels (NaChBac and some others) are frequently used in biophysics as simplified models of mammalian calcium and sodium channels. We report an experimental, analytic and numerical study of the effects of Qf and bulk ionic concentrations of Ca2+ and Na+ on conduction and selectivity of NaChBac channels, wild type and Qf -varied mutants. Methods. Site-directed mutagenesis and voltage clamp recordings were used to investigate the Na+ /Ca2+ selectivity, divalent blockade and anomalous mole fraction effect (AMFE) for different NaChBac wild type/mutants channels and the properties dependence on Qf . Experimental results were compared with Brownian dynamics simulations and with analytic predictions of the ionic Coulomb blockade (ICB) model, which was extended to encompass bulk concentration effects. Results. It was shown that changing of Qf from –4e (for LESWAS wild type) to –8e (for LEDWAS mutant) leads to strong divalent blockade of the Na+ current by micromolar amounts of Ca2+ ions, similar to the effects seen in mammalian calcium channels. The BD simulations revealed a concentration-related logarithmic shift of the conduction bands. These results were shown to be consistent with ICB model predictions. Conclusions. The extended ICB model explains the experimental (divalent blockade and AMFE) and simulated (multi-ion bands and their concentration-related shifts) selectivity phenomena of NaChBac channel and its charge-varied mutants. These results extend the understanding of ion channel selectivity and may also be applicable to biomimetic nanopores with charged walls.

The highly selective permeation of ions through biological ion channels is an unsolved problem of noise and fluctuations. In this paper, we motivate and introduce a non-equilibrium and self-consistent multi-species kinetic model, with the express aims of comparing with experimental recordings of current versus voltage and concentration and extracting important permeation parameters. For self-consistency, the behavior of the model at the two-state, i.e., selective limit in linear response, must agree with recent results derived from an equilibrium statistical theory. The kinetic model provides a good fit to data, including the key result of an anomalous mole fraction effect.

Results of modeling of the wave propagation, impact, and damage detection in a sandwich honeycomb plate using piezoelectric actuator/sensor scheme are reported. A finite element model of honeycomb sandwich panel that reproduces accurately experimental setup and takes into account main characteristic features of the real composite panel, impactor, lead zirconate titanate actuator, and sensors is developed. The impact is simulated to obtain damage with parameters close to those observed in the experiment. Both in simulations and in experiment, the voltage signal of a given shape is applied to the lead zirconate titanate actuators to excite acoustic wave, and the electrical signals collected from the lead zirconate titanate sensors mounted to the panel are used to study wave propagation in the sandwich panel. The results of simulation are shown to be in good agreement with the experimental results both before and after the impact. Properties of acoustic wave propagating in composite sandwich honeycomb panels are discussed.

The highly selective permeation of ions through biological ion channels can be described and explained in terms of fluctuational dynamics under the influence of powerful electrostatic forces. Hence valence selectivity, e.g. between Ca2+ and Na+ in calcium and sodium channels, can be described in terms of ionic Coulomb blockade, which gives rise to distinct conduction bands and stop-bands as the fixed negative charge Qf at the selectivity filter of the channel is varied. This picture accounts successfully for a wide range of conduction phenomena in a diversity of ion channels. A disturbing anomaly, however, is that what appears to be the same electrostatic charge and structure (the so-called EEEE motif) seems to select Na+ conduction in bacterial channels but Ca2+ conduction in mammalian channels. As a possible resolution of this paradox it is hypothesised that an additional charged protein residue on the permeation path of the mammalian channel increases |Qf | by e, thereby altering the selectivity from Na+ to Ca2+. Experiments are proposed that will enable the hypothesis to be tested.

We report a development of probabilistic framework for parameter inference of cryogenic two-phase flow based on fast two-fluid solver. We introduce a concise set of cryogenic correlations and discuss its parameterization. We present results of application of proposed approach to the analysis of cryogenic chilldoown in horizontal transfer line. We demonstrate simultaneous optimization of large number of model parameters obtained using global optimization algorithms. It is shown that the proposed approach allows accurate predictions of experimental data obtained both with saturated and sub-cooled liquid nitrogen flow. We discuss extension of predictive capabilities of the model to practical full scale systems., Comment: 15 pages, 10 figures

We report on progress in development of model-based optimization methods for the autonomous control of the propellant loading system. We briefly discuss properties of the models and demonstrate examples of their validation using the experimental data obtained at NIST and at Kennedy Space Center. We consider application of the modelbased optimization methods to the analysis of chilldown and identification and evaluation of the faults in the cryogenic transfer line. It is shown that model-based optimization provides an efficient tool for the development of autonomous control of cryogenic loading operations.

We report on a progress in development of a hierarchy of two-phase flow models that can accurately predict cryogenic fluid dynamics in real time. We provide details of the separated two-phase cryogenic flow model, which is one of the key components of the hierarchy. We discuss the stability and speed of the algorithm and demonstrate a good agreement of the model predictions with experimental data. We discuss progress in developing of a set of tools for parametric studies and optimization of the two-phase flow in cryogenic transfer lines. We provide examples of the sensitivity study and optimization of parameters for the model of a chilldown experiment.

The conduction and selectivity of calcium/sodium ion channels are described in terms of ionic Coulomb blockade, a phenomenon based on charge discreteness, an electrostatic exclusion principle, and stochastic ion motion through the channel. This novel approach provides a unified explanation of numerous observed and modelled conductance and selectivity phenomena, including the anomalous mole fraction effect and discrete conduction bands. Ionic Coulomb blockade and resonant conduction are similar to electronic Coulomb blockade and resonant tunnelling in quantum dots. The model is equally applicable to other nanopores.

A Bayesian inference technique, able to encompass stochastic nonlinear systems, is described. It is applicable to differential equations with delay and enables values of model parameters, delay, and noise intensity to be inferred from measured time series. The procedure is demonstrated on a very simple one-dimensional model system, and then applied to inference of parameters in the Mackey-Glass model of the respiratory control system based on measurements of ventilation in a healthy subject. It is concluded that the technique offers a promising tool for investigating cardiovascular interactions.

We analyse the non-equilibrium distribution in dissipative dynamical systems at finite noise intensities. The effect of finite noise is described in terms of topological changes in the pattern of optimal paths. Theoretical predictions are in good agreement with the numerical results.

The energy-optimal migration of a chaotic oscillator from one attractor to another coexisting attractor is investigated via an analogy between the Hamiltonian theory of fluctuations and Hamiltonian formulation of the control problem. We demonstrate both on physical grounds and rigorously that the Wentzel–Freidlin Hamiltonian arising in the analysis of fluctuations is equivalent to Pontryagin's Hamiltonian in the control problem with an additive linear unrestricted control. The deterministic optimal control function is identified with the optimal fluctuational force. Numerical and analogue experiments undertaken to verify these ideas demonstrate that, in the limit of small noise intensity, fluctuational escape from the chaotic attractor occurs via a unique (optimal) path corresponding to a unique (optimal) fluctuational force. Initial conditions on the chaotic attractor are identified. The solution of the boundary value control problem for the Pontryagin Hamiltonian is found numerically. It is shown that this solution is approximated very accurately by the optimal fluctuational force found using statistical analysis of the escape trajectories. A second series of numerical experiments on the deterministic system (i.e. in the absence of noise) show that a control function of precisely the same shape and magnitude is indeed able to instigate escape. It is demonstrated that this control function minimizes the cost functional and the corresponding energy is found to be smaller than that obtained with some earlier adaptive control algorithms.

The ability of the potassium channel to conduct K+ at almost the rate of free diffusion, while discriminating strongly against the (smaller) Na+ ion, is of enormous biological importance [1]. Yet its function remains at the center of a “many-voiced debate” [2,3]. In this presentation, a first-principles explanation is provided for the seemingly paradoxical coexistence of high conductivity with high selectivity between monovalent ions within the channel. It is shown that the conductivity of the selectivity filter is described by the generalized Einstein relation. A novel analytic approach to the analysis of the conductivity is proposed, based on the derivation of an effective grand canonical ensemble for ions within the filter. The conditions for barrier-less diffusion-limited conduction through the KcsA filter are introduced, and the relationships between system parameters required to satisfy these conditions are derived. It is shown that the Eisenman selectivity equation is one of these, and that it follows directly from the condition for barrier-less conduction. The proposed theory provides analytical insight into the “knock-on” [1] and Coulomb blockade [4] mechanisms of K+ conduction through the KcsA filter. It confirms and illuminates an earlier argument [3] that the “snug-fit" model cannot describe the fast diffusion-limited conduction seen in experiments. Numerical examples are provided illustrating agreement of the theory with experimentally-measured I-V curves. The results are not restricted to biological systems, but also carry implications for the design of artificial nanopores.

We report the progress in the development of the chilldown model for a rapid cryogenic loading system developed at NASA-Kennedy Space Center. The nontrivial characteristic feature of the analyzed chilldown regime is its active control by dump valves. The two-phase flow model of the chilldown is approximated as one-dimensional homogeneous fluid flow with no slip condition for the interphase velocity. The model is built using commercial SINDA/FLUINT software. The results of numerical predictions are in good agreement with the experimental time traces. The obtained results pave the way to the application of the SINDA/FLUINT model as a verification tool for the design and algorithm development required for autonomous loading operation.

Fluctuational escape from a multiwell potential is shown to display new features, as compared to the conventional single-well case. The flux J may depend on friction Gamma exponentially strongly, over an exponentially long period; for small enough temperatures, J(Gamma) undergoes marked oscillations in the range of small Gamma, and the time evolution of J changes drastically as Gamma exceeds a critical value.

We investigate, theoretically and by analog experiment, the distribution of paths for large fluctuations away from a stable state. We have found critical broadening of the distribution of the paths coming to a cusp point that represents the simplest generic singularity in the pattern of most probable (optimal) fluctuational paths in nonequilibrium systems. The critical behavior can be described by a Landau-type theory. We predict and observe two-ridged distributions for arrivals on a switching line that separates the areas reached along optimal paths of different types.

A new type of non-linear resonance is reported. It possesses an unusual counterintuitive feature, namely that: strong non-linear response to a weak periodic force can be obtained in the absence of exact resonance between frequency of the force and any eigenfrequency of the system. It is shown that the topology of phase trajectories differs substantially from the case of conventional non-linear resonance. The frequency of a driving force at which the transition between the conventional non-linear resonance and the zero-dispersion one takes place is found. Possible applications are discussed.

The flow of ions through a biological ion channel can be considered as transitions between occupied energy levels in the channel and either of the connecting bulk reservoirs [2]. Discreteness of ions and an electrostatic exclusion principle ensure that the number of channel energy levels equals the number of occupying ions. Using these fundamental physical principles we have recently introduced [1] an ionic Coulomb blockade (ICB) theory developed by analogy with the similar phenomenon of electron tunnelling in quantum dots [2,3]. In this picture channel selectivity is governed by energy level changes [1]. We present details of the ICB theory for ion transitions through the channel. It incorporates physiological solutions and channel properties: physical dimension, voltage drop and fixed charge, and hence allows for comparison with physiological data. The set of kinetic equations obtained using ICB is analysed. The channel probability of occupancy as a function of transition rates (and hence fixed charge and number of ions) is obtained in the steady-state approximation. It is shown that this probability displays the staircase structure familiar from analysis of occupancy in quantum dots. It is also shown that current through the channel displays sharp peaks as a function of fixed charge, hence relating channel selectivity to the structure and position of energy levels. The contribution of hydration energy is also discussed. We anticipate that inclusion of this energy into ICB theory will provide an important insight into the selectivity and conductivity of ion channels.

In a modern world, importance of computer modeling for solving complex engineering problems cannot be overstated. However, in a number of critical engineering problems computational models cannot provide unique answer and so further physical and analytical insight is required to guide computer simulations. Such an insight becomes even more valuable when off-nominal regimes of operation have to be considered. To deal with complexity of the physical process at the interface of multiple engineering systems a new discipline is emerging – operational physics of critical missions. This discipline combines an old-good physics based approach to modeling engineering problems with modern advanced technologies for analyzing continuous and discrete information flow involving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. In this paper the new approach is illustrated using as an example analysis of the critical physics phenomena that lead to Challenger accident including physics of cryogenic explosion and propagation of detonation waves, internal ballistics of SRM’s in the presence of the case breach fault, and monitoring of the structural integrity of the spacecraft.

An engineering assessment of the stage separation fault is reported for two-stage, vertically stacked space vehicle. The analysis combines explicit modeling of the fault evolution failure with analytical estimations based on simplifie physics-of-failure models. The following sequence of events is analyzed: (i) structural dynamics of the nozzle extension during the impact; (ii) yielding and burning through the damaged nozzle under the plume loading during engine start up; and (iii) reduction of the actual thrust and side load in the quasi-steady burning regime. The analysis reveals characteristic time-signatures of the impact-induced torque and lay down foundation for the development of a diagnosis and prognosis system for the stage separation fault.

High-Fidelity Model of the sandwich composite structure with real geometry is reported. The model includes two composite facesheets, honeycomb core, piezoelectric actuator/sensors, adhesive layers, and the impactor. The novel feature of the model is that it includes modeling of the impact and wave propagation in the structure before and after the impact. Results of modeling of the wave propagation, impact, and damage detection in sandwich honeycomb plates using piezoelectric actuator/sensor scheme are reported. The results of the simulations are compared with the experimental results. It is shown that the model is suitable for analysis of the physics of failure due to the impact and for testing structural health monitoring schemes based on guided wave propagation.

An analysis of the case breach fault in a large segmented SRM is presented in the context of development of the IVHM system. The internal ballistic of the SRM is simulated using a 1D model that takes into account grain geometry, propellant regression rate including erosive burning and surface friction, nozzle ablation, and case breach fault dynamics. The model is integrated in quasisteady approximation by solving a boundary value problem for the spatial distribution of the flow variables in the combustion chamber at each time step of steady burning. The model can simulate very accurately nominal and off-nominal regime of internal ballistic of segmented SRM and can be applied to an analysis various fault modes of large SRM. The model calculations are verified by comparison with the results of simulations of axi-symmetric high-fidelity model (developed by the third party). The model is used to simulate case breach fault at a given location along the motor axis. The fault diagnostic and prognostic (FD&P) system is developed in two steps. First, the diagnostics of the case breach fault is performed using stationary solution for the nozzle stagnation pressure, which is known to hold surprisingly well in large SRMs. The later approximation is further improved by introducing an effective design curve that relates the total burning area to the propellant burn distance. The prognostics of the case breach fault dynamics and internal ballistics of SRM in off-nominal regime is achieved using scaling equations developed earlier for malfunction study of RSRM ballistic failure. The results of these predictions are compared with the results of integration forward in time 1D model of internal ballistics of SRM in off-nominal regime for the given parameters of the case breach fault.